From Virus to Population: Multi-Scale Stochastic Modeling Reveals Mutation-Driven Acceleration of Infection Dynamics

From Virus to Population: Multi-Scale Stochastic Modeling Reveals Mutation-Driven Acceleration of Infection Dynamics | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article From Virus to Population: Multi-Scale Stochastic Modeling Reveals Mutation-Driven Acceleration of Infection Dynamics Yathu Krishna Y K This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7728221/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Predicting the course of epidemics and developing effective interventions depend on an understanding of how viral mutations affect infection dynamics at various biological scales. Here, we provide a thorough in silico investigation into the effects of viral mutations on infection progression by integrating population-level SIR modeling, immune response, multi-strain dynamics, and stochastic intracellular viral simulations. Stochastic simulations demonstrated that even slight mutation-induced increases in viral production or infectivity at the intracellular level resulted in significantly greater peaks in the number of infected cells. The amplification potential of minor genetic alterations was demonstrated by the fact that wildtype strains attained an average peak of around 2,680 infected cells, whereas mutant strains had an average peak of about 8,070 cells. The significance of random fluctuations in early infection dynamics was underscored by the models' capacity to capture underlying stochastic variability. It was discovered that mutations that accelerated intracellular infection directly translated into larger and faster epidemics when the intracellular viral load was coupled to a population-level SIR framework. In particular, mutant strains raised the effective reproduction number (R0) from 3.0 to 4.5, resulting in an earlier epidemic peak at about 24 days and a peak infected individual count of about 4,430. The robustness of these effects was further shown by sensitivity studies, which showed that infection peaks were extremely responsive to variations in viral generation and infectivity. All together, our multi-scale modeling methodology shows how minor cellular-level mutation-induced alterations can spread to affect epidemic outcomes at the population level. The significance of stochasticity in infection dynamics, the potential for early intervention measures to reduce intracellular viral amplification and epidemic development, and mechanistic insights into viral evolution are all highlighted by these findings. A strong computational tool for investigating the effects of viral mutations and guiding public health interventions is provided by this integrated platform. Virology Epidemiology Statistical Epidemiology Bioinformatics Computational Biology Systems Biology Population Biology multi-scale modeling stochastic viral dynamics intracellular infection viral mutation multi-strain simulation epidemic modeling SIR model immune response treatment intervention peak infection population-level transmission 1. Introduction Complex dynamics spanning several biological scales, from intracellular processes to population-level epidemiology, are displayed by viral infections. These dynamics are frequently simplified by traditional models, which may leave out important interactions and variability. In an effort to close these gaps, recent developments in mathematical modeling have integrated hierarchical scales, multi-strain interactions, and stochastic aspects to offer a more complex understanding of viral evolution and propagation [1,2]. Viral replication is prone to intrinsic stochastic variations at the cellular level. Even under the same circumstances, these variations can result in a considerable degree of variation in infection outcomes. Research has shown that models of viral replication that include stochastic processes are better able to capture observable phenomena, like the variation in viral loads among infected cells [3,4]. This method differs from deterministic models, which could miss the subtleties of viral mutant emergence and early infection dynamics. Complexity is increased when a population has several different virus strains. The course of an epidemic can be influenced by interactions between strains, such as co-infection and competition. These relationships have been examined in recent models, which show how mutations can change the fitness landscape of viral populations and impact the dynamics of transmission [5,6]. These results highlight how crucial it is to take into account several strains in epidemiological models in order to precisely forecast the development of disease and guide control measures. Understanding epidemic consequences at the population level requires integrating intracellular dynamics and multi-strain interactions. Understanding how mutations might affect the fundamental reproduction number (R₀) and the overall trajectory of an epidemic has been made possible by models that connect within-host processes to between-host transmission dynamics [7,8]. By taking into consideration the entire range of viral dynamics, these integrated models aid in the creation of more potent public health treatments. Accurately capturing the intricacies of viral infections is still difficult, despite modeling breakthroughs. Additional levels of unpredictability are introduced by the interaction of immunological responses, mutation, and stochasticity, which can affect the course of epidemics. In order to improve models that take these variables into account and create tactics that can lessen the effects of viral infections on cells and populations, more research is required [9, 10]. 2. Materials and Methods 2.1 Module 1: Optimized Multi-Scale Viral Dynamics Modeling A deterministic-stochastic-population modeling pipeline was put into place in order to capture the dynamics of viral infection at various biological scales. 2.1.1 Intracellular deterministic dynamics. At the intracellular level, we described target cells (T), infected cells (I), and free virions (V) using a system of ordinary differential equations (ODEs). The equations adhere to accepted formulations of viral dynamics [11,12]: where β is the infection rate, δ the infected cell death rate, p the per-cell virus production rate, and c the clearance rate. The ODE system was solved numerically using scipy.integrate.odeint (Python). 2.1.2 Stochastic intracellular dynamics. Given the intrinsic noise of viral replication at tiny sizes, we used a stochastic simulation in accordance with Gillespie-style event-based techniques [13,14]. Infection, cell death, virion generation, and clearance are all reactions that happen with a probability that corresponds to their propensity. Exponential distributions were used to calculate waiting times. Poisson-tau leaping was also used to test faster approximations [15]. 2.1.3 Population-level dynamics. We expanded the model to a Susceptible–Infected–Recovered (SIR) system at the epidemiological scale [16,17]. The population model that was deterministic was: where N is population size and γ is the recovery rate. Basic reproduction number (R0) and peak infection statistics were extracted to connect intracellular parameters with epidemic outcomes [18]. 2.2 Module 2: Fast Stochastic Simulation with Mutation Effects Scaling factors (1–1.5×) for β and p were introduced in order to investigate mutation-driven variations in viral infectivity and production. Stochastic Poisson approximations were used to simulate each mutant strain [15,19]. In order to represent genetic drift and selective advantage situations in viral evolution, variability was captured by averaging many simulations [20]. 2.3 Module 3: Multi-Strain Viral Dynamics with Immune Response and Treatment Host immunity and therapeutic intervention were incorporated into a two-strain stochastic model. Immune clearance. An adaptive immune response was modeled as an increase in viral clearance rate (𝑐) after immune activation time [21]. Treatment effects. Antiviral treatment was simulated as fractional reductions in β and p after a specified onset time [22,23]. Mutation effects. The mutant strain was assigned enhanced infection and production rates, consistent with immune escape and fitness advantage mechanisms [24]. Infection, death, production, and clearance events were sampled from Poisson distributions at each timestep, and parameters were continuously modified to account for treatment and immunological effects. This paradigm made it possible to evaluate the timing of interventions on peak viral levels and analyze competition between wildtype and mutant strains [25, 26]. 2.4 Module 4: Full Multi-Scale Viral Dynamics Analysis In order to connect intracellular stochastic viral dynamics with population-level epidemic consequences, we employed a hybrid multi-scale modeling methodology in this module. A stochastic τ-leaping approach was used to describe intracellular viral particle (V), infected cell generation (I), and target cell infection (T) [13,15,17]. The inclusion of distinct compartments for wildtype and mutant strains allowed for the measurement of infection rate (β), viral generation rate (p), and clearance rate (c) specific to each strain. Scaling the wildtype base parameters with a multiplicative factor (1.5×) for the mutant strain allowed for the incorporation of mutation effects, which reflected increased replication and infectivity [4,23,24]. A time-dependent clearance function was used to boost viral particle clearance after an immunological onset threshold (day 3) in order to account for immune response dynamics [1,21]. Day 2 saw the start of antiviral therapy, which was modeled as a proportionate decrease in both β and p [25]. To capture the variability in viral load and infected cell peaks, ten stochastic realizations were simulated for each scenario. The results were presented as mean ± standard deviation. Using parameters scaled by the average intracellular viral load of the mutant strain, the model was connected to a classical SIR framework at the population level [16,18]. An emergent fundamental reproduction number (R₀) was obtained by adjusting the effective population transmission coefficient (β_pop) to account for increased infectivity. Odeint from SciPy was used to solve the ODEs numerically [2,12]. Lastly, a sensitivity analysis was conducted over a range of β and p values, and the results were assessed in terms of the time to clearance and the maximum number of infected cells [6,7,26]. This method made it possible to measure the extent to which mutation-driven intracellular advantages lead to epidemic-level consequences. 2.5 Module 5: Integrated Multi-Scale Viral Dynamics Flow We created an integrated multi-scale pipeline to expand Module 4, which methodically linked deterministic population-level epidemic trajectories with stochastic intracellular dynamics. There were six consecutive steps in this pipeline: Intracellular viral dynamics are started with two competing strains (mutant and wildtype). Poisson sampling of infection, clearance, and viral production events is used in a stochastic simulation of intracellular viral dynamics over ten replicate runs [13,14]. Peak viral loads for each strain are quantified and summarized as mean ± standard deviation across simulations [9,20]. Intracellular results were propagated into a population-level SIR framework, where the transmission parameter (β_pop) was directly scaled by the mutant strain's increased viral production rate [18,19]. Coupled ODEs computed with odeint are used for deterministic epidemic modeling at the host population level [2,16]. Time-to-peak, epidemic peak size, and R₀ were important outputs [11,22]. Global sensitivity analysis is used to evaluate the robustness of both within-host and between-host results by altering intracellular parameters (β, p) throughout biologically relevant ranges [5,23]. This integrated method aligns with current frameworks for multi-scale infectious illness modeling [3,6,10,19] by allowing a bottom-up perspective that links emergent epidemiological trends with molecular-scale alterations. 3. Results The paradigm for multi-scale viral dynamics offered thorough insights into the intracellular and population-level behavior of both wildtype and mutant viral strains. Around day 38.2, the pandemic peaked at 3008 infected people, and the system generated a basic reproduction number (R₀) of 3.00 at baseline. The kinetics of intracellular infection changed significantly when mutation effects (mutation factor = 1.5) were added. In the stochastic simulations, the mutant strain quickly grew to a significantly higher peak of 7299 infected cells at day 1.0, while the wildtype strain peaked at 2683 infected cells. The robustness of this divergence was validated by replicate stochastic simulations, which produced mutant peak values of 8069.1 ± 1693.2 and wildtype peak values of 2680.0 ± 1208.9. According to these results, the mutant strain continuously maintains greater infection loads in host cells. The effective reproduction number increased to R₀ = 4.50 at the population level when the intracellular mutant dynamics were coupled into an epidemic model. The epidemic trajectory was sharper, peaking at 24.2 days with 4431 infected individuals, which was significantly earlier and larger than the baseline epidemic peak. The way that small-scale mutational advantages result in larger-scale epidemic amplification is highlighted by this acceleration. Sensitivity testing of infection rate (β) and viral production rate (p) in addition to the fundamental intracellular and population analyses showed that increases in either parameter resulted in higher and earlier infection peaks, with β = 0.0007 and p = 100 producing the steepest and most severe trajectories when compared to lower parameter combinations respectively. Activated on day three, the immune response module resulted in higher clearance rates, which in some runs delayed progression and significantly decreased viral loads. The introduction of treatment on day two, which was modeled as a 50% drop in infection and production parameters, decreased the spread of both wildtype and mutant strains but did not completely eradicate infection; in all studied settings, the mutant strain remained dominant. These investigations collectively reveal a number of significant trends: Epidemic outcomes are highly sensitive to infection and production parameters, with relatively small increases driving disproportionately larger infection peaks; (i) mutation accelerates both infection peaks and epidemic spread; (ii) immune response and treatment reduce viral burdens but are insufficient to overcome mutant advantages; and (iv) stochastic intracellular dynamics reveal strong variability, but mutant strains consistently outcompete wildtype. Discussion New biological insights into how viral mutations affect infection outcomes at the intracellular and population levels are offered by the multi-scale stochastic and deterministic simulations that are provided here. Our results highlight the disproportionately enormous effects that even little changes in viral characteristics can have on disease dynamics. In particular, inserting a 1.5× mutation factor in viral production (p) and infection rate (β) reliably increased the severity of infection, leading to significantly higher peaks of infected cells in the host and faster epidemic propagation in the population model. These findings support the evolutionary advantage provided by mutations that increase viral fitness by demonstrating how seemingly insignificant genetic alterations at the molecular level can scale upward to alter the trajectory of epidemics. The robustness of mutant strain dominance is further demonstrated by our models' integration of immunological responses and treatment interventions. Although therapy started on day 2 and immune activation started on day 3 greatly decreased viral loads, these actions did not remove the competitive advantage of more contagious strains. This implies that although prompt interventions are still essential, they might not be enough to stop the faster dynamics of fitter viral variants unless they are paired with tactics that target mutation-driven amplification explicitly. Our multi-run stochastic simulations, which demonstrated significant variation in peak infection levels across multiple runs under identical settings, provide another important insight. This stochastic heterogeneity closely resembles clinical data where patients show different infection courses even though their exposure and risk variables are comparable. Because deterministic frameworks alone are unable to capture this real-world unpredictability, such variability highlights the significance of incorporating stochastic features in models of viral infection. When intracellular results were scaled to the population level, it became clear that mutation-driven effects directly translated into epidemic behavior. In addition to increasing the effective reproduction number (R₀), mutant strains also accelerated the onset of epidemic peaks and boosted the overall number of infected people. The idea that evolutionary advantages gained at the cellular level can spread to the population level, leading to more severe epidemic outcomes and making control efforts more difficult, is supported by these findings. Lastly, the sensitivity analyses show how important viral production (p) and infection rate (β) are in determining outbreak intensity and persistence. Even small adjustments to these factors can have a cascade effect on the dynamics of an epidemic, making them useful leverage points within the viral life cycle. We discovered the circumstances in which viral amplification is greatest by methodically altering these parameters, which may provide direction for therapeutic targeting and risk evaluation of new variations. When combined, these findings offer novel biological insights in the form of model-based predictions, going beyond simple computational exercises. Our paradigm illustrates how minor genetic alterations can have significant impacts on viral evolution and epidemic spread by connecting intracellular stochastic processes, immunological and therapeutic effects, and epidemic-scale transmission dynamics. 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09:12:59","extension":"html","order_by":32,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":51886,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-7728221/v1/ae9e52db100b526e01e3ff38.html"},{"id":92490657,"identity":"68e59ffb-1ed4-4f9a-a96c-250c15984e4b","added_by":"auto","created_at":"2025-09-30 09:37:03","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":497506,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7728221/v1/f7c74753-580c-447b-bd64-414489cd1425.pdf"},{"id":92489012,"identity":"981b8e33-3e3b-4afe-b81a-89b7bebc6592","added_by":"auto","created_at":"2025-09-30 09:12:59","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":846855,"visible":true,"origin":"","legend":"","description":"","filename":"SupportingFigures.docx","url":"https://assets-eu.researchsquare.com/files/rs-7728221/v1/d4a6d86d70c661ff81494c68.docx"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eFrom Virus to Population: Multi-Scale Stochastic Modeling Reveals Mutation-Driven Acceleration of Infection Dynamics\u003c/p\u003e","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eComplex dynamics spanning several biological scales, from intracellular processes to population-level epidemiology, are displayed by viral infections. These dynamics are frequently simplified by traditional models, which may leave out important interactions and variability. In an effort to close these gaps, recent developments in mathematical modeling have integrated hierarchical scales, multi-strain interactions, and stochastic aspects to offer a more complex understanding of viral evolution and propagation [1,2]. Viral replication is prone to intrinsic stochastic variations at the cellular level. Even under the same circumstances, these variations can result in a considerable degree of variation in infection outcomes. Research has shown that models of viral replication that include stochastic processes are better able to capture observable phenomena, like the variation in viral loads among infected cells [3,4]. This method differs from deterministic models, which could miss the subtleties of viral mutant emergence and early infection dynamics. Complexity is increased when a population has several different virus strains. The course of an epidemic can be influenced by interactions between strains, such as co-infection and competition. These relationships have been examined in recent models, which show how mutations can change the fitness landscape of viral populations and impact the dynamics of transmission [5,6]. These results highlight how crucial it is to take into account several strains in epidemiological models in order to precisely forecast the development of disease and guide control measures. Understanding epidemic consequences at the population level requires integrating intracellular dynamics and multi-strain interactions. Understanding how mutations might affect the fundamental reproduction number (R₀) and the overall trajectory of an epidemic has been made possible by models that connect within-host processes to between-host transmission dynamics [7,8]. By taking into consideration the entire range of viral dynamics, these integrated models aid in the creation of more potent public health treatments. Accurately capturing the intricacies of viral infections is still difficult, despite modeling breakthroughs. Additional levels of unpredictability are introduced by the interaction of immunological responses, mutation, and stochasticity, which can affect the course of epidemics. In order to improve models that take these variables into account and create tactics that can lessen the effects of viral infections on cells and populations, more research is required [9, 10].\u003c/p\u003e"},{"header":"2. Materials and Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n \u003ch2\u003e2.1 Module 1: Optimized Multi-Scale Viral Dynamics Modeling\u003c/h2\u003e\n \u003cp\u003eA deterministic-stochastic-population modeling pipeline was put into place in order to capture the dynamics of viral infection at various biological scales.\u003c/p\u003e\n \u003cdiv id=\"Sec4\" class=\"Section3\"\u003e\n \u003ch2\u003e2.1.1 Intracellular deterministic dynamics.\u003c/h2\u003e\n \u003cp\u003eAt the intracellular level, we described target cells (T), infected cells (I), and free virions (V) using a system of ordinary differential equations (ODEs). The equations adhere to accepted formulations of viral dynamics [11,12]:\u003c/p\u003e\n \u003cp\u003e\u003cimg 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zEEt70r/XgFUreyJu7NN8Y0IioHMzAxZWQq3y6xw8qiEky6ZSCrSsH5X2gdWxMPdBauHS4pLicLKFkfnxgTWd8fRFnJktnh7eeBgGpaQKSmXeJTTXuP5fclomlTzwKWYU6yW7l/lvyjvAusvWNI8oAmVTSIfaSkRxFlUwTolEddWjWhQ0+1RY6JJSeTa2WvQoB5VPR6GWgGdDiN6vHy8Hl0q7+OLtZkcfWI6WQV3PpDDvp/mkj1yCj1LKx5bJuURe2UfV439GVzL5LKIIOSawLa2F5bxydQf+hIFqXKNnN1/AHk5O7yaBGF6DOjdrAx8a/oWXHBypbxLRUhKJ0NbNFU4XN+wmNPVO9KvVY1SCHPKcK7SGj+bU0yftpEEfdHTPwoYIsOIvHUDfcs2+NkUb8Mm+RsMWmKP7yfV2QPPgHqYnpvxIvDyKYeNDSSmpN+fwjClvcKM2aEMGD+QGlZPqHjPmdRplrCcC2EYKzjg5edGXk4WmVn3UKVdY9+mrchbd8W/dmc6+VXH/dEmREFqShQXQqFpQFW8PQoqhkGY4+ziReOqJmNFjyr4ys3QZUaTVHAVgMx937E0vjdTX/1zEnTJ/0/kZnP7XBhVX2+JTH+PjLRMstUqItf9xG55U4a+0QIHy3Z0M+1QDREcPaGlvK07bYIKr3LLV7jRpZ7JU005Z9wdK2CljeF2Th5G05tv7mXFAS0vdehM1VKa9zd39KRLJw9OL/yc71af41Fa1iJirkSTeENDg/ZBuJrmp5M8R4Kc1GscDj7GjYw8APISrrF/5w5ORCRTdFc8gFGbxdn9VylXyZ2ABiYPayVJnUzEmQNs3bGf0Ji7hYpcPbywtLYhK+Y2eYV6TSPnFi4mLPAt+vg7l1jEQuo0S5SGq9e1ONk6k/XHNN5+fQCDBg6g75CxbLjdjMmfjeS1QR1o4V+dgjSWOSRFHOek8CWwRm08TKKtcjt3mvb6hHYeBdco74KrDHS6OJJSTK7fO8KUNXd4/fPeuEv/9edKrYnjSnR1AuWHmNL/NV4fOIjBQ/ozcMYdhs+YxfBW1en41iuY/puIPcruJBn27h1p4mlaAJW6fM2g+qapG2xxsLbHhtskJGkKGj6Rwh879qOv14aOTUsndGDUx7Fx7g/syvGji3cyS36cx+6w7KK3AalcjogiJqcSnRq7YS3NCRSL/PTrHF6ygm07fmPK9LmsWvwLq/edJjriKrsXf80P60PRFnmNNusYweds8HSuRaPaRQqLnYaoo6uY+NXPbDt9mfCIcLbM/Yx5B249usPGoTxypRLjjdskmXSamsu/sTrclWE9m+JkGqopZsW+erbUGPOJOzCfyZsisFA8Sy8hAB8GTfqYFq7FtPHDcIPfluxEU6krXZ3jOHw2ArW1Pfr0K+w7omPwz7Pp51vks1XxrP0wkDeCg5i1fDkfdSh0UNpjXGdyYEvm3/Xgm10XeLcWgJrDX3/EJrfBfPd2C+z/ow/5+WFrGbf4aOFkGk9kRKspT7f3R/NKg0pP3QqUcXkOo9bVY/EnrhzecIB4LLCxvcf+xYeoMG4+M3tVKfoSkpd3p/YnZ6j69jbOf/uYHLuFaDgw7R1GfLGKoN+iWD64OhZAypk1zFweQftJU+nsVvQ1JUAdyqwPxrNDdGXa+JfJ3v0NA8fupPvC7cx+t1XB/lqAzBC+eXcAXx8NYvexeXStISUFAMiIPsiKn1cSrrdE8ZdDJYHRzBLf7uMY39m7aCGQT8zBRcy95Me7/ucZ3m8CeZ0nMm3SOLrVtCFs2RA6fKdl6pY1vO1X8Fh+Z9s7VBu4h6bv/MKemS8VWi1cvPKI2DWLd78+RK3+Y/l8ZDdsz39LuwHfIe+wnFPLe9+fbkj5nd7dPuBgYnf2JS2giVwG+lgWT55LWp3+jH09iJIM9pfdTlMYUCVFcPHmXeTPtF9MAPZUq1+XCo/2ZT1nt4+wePsRHLtM4tVqBZd1d67xRfd2hLVbxcbvOhZKD6dOOsH4li3ZWGUkK5bNp1uRUcmfZbK8tx8fhtgxbMlFZnWxRn16Dh9syGP4x2NoUqkEH8leMMbMG5yNTsH4TDVeYDRYUKlWbbydbJ4SkjFybelrLK60htmdC88oHvyoDoMP9mJv2FT8CpWoWD+oMaP2pjNgdQJzi7zucS7/+h5DPv4F8dFxTk9qgXV2LKt+nMj1gO/5pm/BnHbJ0XHk8568ud6RX0NW09FJRsrRZQzvN4z0t7axZXJPPEx+rdzLGxk58DU2V5vNuV8/pHYZ3Xf9d+XfS+J6RAxZRjnP0kwJmRwHTz/8PB6zFURzj2NLxhHZdQH1D42k16dRjPl9DWNbeyHDwO3DX9OwxzZ6zNnEkrcK5goOjatKt3UWDJl7lEV9/+qh/Pm5G7mV0R2GEdnlO9YseIfqSlCd/pFXxp2n17dzeL/1g+iJ9hQfthrCymsVmBd5nDfcIeqPn/nlkJFBkz8isFzRdy5exdppTpw4kQ0bNmBt/fwz+8hkMkJCQrC0LLnzeAx5t/h1eDdmXTJD+eRWFABjfi5Ovb9j3Rf98HjQCyaf3sG2/VG0+uJj6pi8Xp8exbSezTgeMJ91C143OXTbyJ1zs+nceBIOw75l+ZL3+fOY5c/2jPKi10YFL31/jC2Ds/np42XQaigfvFL7qSOmktahQweSkpKQy//5s61KpWLLli0EBv75MLFiJdJZN2wMlt+voleRjuDkF/UZsCKQNQlLaWFaoD3JyEYD2ZRSl1/Dd/DKM3Qgt7d8Qv/RPxLWeRPJi3qSsu97Pt9didkLh1Cx6M1Pos8jeHJbRm9RoZT/RQuty0PdYDTbZo3E73GRl5iVdOg5hvTeu7g4pQlmgOH6Dt59oydhbTfz+5TeuD/qNI1c3TyVwa9+jcPkrayd+ApupRyeXbx4MdOnT8fOrnhOMTcajTg5OXHs2LGiRcVHGMnPU2MhT2PZ+H68c641h9bNoJW3HEQ+1xf3p/oXtxkzdz0z+z98ao9iYo3mLDFWY9qeM7xt8jD/WPdOMWHUl2w7m4TS4mn/RIEuX0nNlu8zb+kwKhUt1mdx5NvetJ2Vz9QVq/m8x/2WTRjyycnWYuloZ7KoLYoprfowOzSTcceTmOgawg9zf8Gy24+MblXyy5aKtdPU6XQYCmU8fr6e3mEK8rNTSbmb/8TVfH9mQXk3V2yfmCVeoNfmoy+0EuMp5AosFPIHE9Qqzu1dz/6zlRn3dYdCqyVV8fsZ0XAQmW8sYu3MngV5WEU+0Qv7UOPjWIZOXcGysY1NXvVkN+a3o/ZXN+n21Sq+8zjK0suuvPPFcKq9YIPM/Px8nmf1UyqVmJk9+WnGqM4kMUP15xV4jyUQRgX2Li6Us1Y8cZGByNvH6P6xfLrtvSINQxZLezXni9DO7Lg5i4amRed/IrDfdOJ9viH84Pu4mpY9gSFkNt2HfkqwzywSfq7J/HG/Um/OWvr8ZeShMINO84zhacDMHKXC/LEjoIS1b9J5zD56bwpnyoOGS3ttA2+9/imWo9Yz550gk2P/0tj5wwh6j49kwpb1fNnbvxRW+Ram1+vR6/VFLz9XMpkMC4unf+n0mmwyUjPRyMyeWMcKk2HhUIEK9k/+C4rEk3z6RhcOBcxm44/D8FEA2nusH+zOm5dbMmPVTj5s+KDDu72Spg0+Jq3yu+w49w2ma9UeSxjQ6vQYny1cg8zM/H7ShCLXDVlx/NCvCt9r3mLFyqX0eOrRuHlsfqsNo7ZdZ9DaKPom/8TS622YOb1LqRzaUKydZqky5HFt0yTGro3A8pnmNI0IajBq3jQ6uj25Qv7f8hPZvGIW+y1HsmiI6XhRR+yWkbQcEcZbqzYzpatJ06u9y+qB7gy+0JgvF+9kcvtnqyL3tgyl4rAD1AroSNOWTgT1mcrg+k//8oIg904KaitXXMropKfqxFzemnuIfENBOtEnM6DNc6Xv518ysHnlJzby+Se+oOG21oT92LFwQeJqujcbT8Lry7gwo0uh8G7E/N70mPQHVh+c48qXzzgyvr6GXm+MYUf6S0zsnsrNhvNZOaj0VkFH/foqPT9T8W34ZnpVuN893to7gzcnHuaNeWsY3syp4OaMq8x+vx1jQtqzeuN83mj4mNGBUU1GejYKByfsLR4zsi2TBCmXtjJr8iKuyqz+ek5TCAzmVtR5fRrf9a5atPSROyFLGNp1Eu5T1zP3vRZYA/kZexlQvQ/X23/J5vWfUv1BhbyzfhB+o/fgOWgdZ2d2LLE927qMaKa8XIOtHl+xes1kAkyaJ6PeiDpbjXV520ffm6NfNqf/wiu49vmITppMOs+eT/vSmhYvnOtAUlwMaeFiSp864pVv9xbKwKONCRbvB7mJruPXiHiT60IIoc09IgZXtBA+rQeJ4HtFCp9CfexrUcFaIZT2VcSwBeeFaU6gJ9He2inGvdpFvP7RPBGZV7RU8iTnp7UWnp2/FDdNL+YnitUjgoR/23fE/jtF//opYsmbLYSrhav4+lxOkbKnuLNPvNHaVyhAVOm1sPDnlYLsQ+NFPdcGYta1rPsXtDFi5ZjWotM7i8WNIr/y3Wv7xJBKCM/XpouzGYXLHko6vESM6NpevDn/mMgs+ieT/A0qcX79u8KRuuKzVaGPrl6c3klYVO8pZp4uXOf+GB4gXJydxahg0zQ7JUCdKFa96SV8u40XIaYfbUgTRzfMEvM2hJlcFCJ8XmfhUU4hLB0DxKd77hQqK2nFmrD9/yF4llHAv09myiVObIxCUT6DkKspZKTFcW7XJtbuO4us4bt89ml/qirAEH+CJYsXsnbbfvZu/o0NJ+JQ683RZN7i1K5QjN4++LjYPWVhCgjFLbb9uBtlz3HM++ZVHp7//TSGyE188NWvnLgShn2bUbTzerFGmy9mvbjF73ND8aiazZHjN0jPTiP6zEF+37iZUNGIkVO/oIunNbL8TEK2zuSHZXs4tm8da7YfJ/auDLkxk7AjJ4hIUlCjvvfTVwDa5HFl7SaO5AYyb80MWjg9wz+1GFl41cDh3hnWbLiAOl/FxV0bCU7xZvhH79PE7f6wIeX4Qr5dtIFtv69h65l4DHI92TcjybavSS1Pe0ynVaP2LGXW3I0cOAsdhnWiSqFMVi+QF7MiFtBkcGr9j2wNz0amNCc7L5FLO35jxWk5wz6dwkft3TDeucz6ZfP4bdMKVq47SWyWGoUxl6T425SrEUiFp1bE50Rhg2tFO67s38LJSC0iL4nzwTvYfuAcqTnm1OzQkWqOBXXAIeMsP266SO1Bv7Lgg3pP/64Us9IPz4pc9kwdwbJLGgxm7nQYMILhveo8MRz276Qh+thC5pxoxvRBcOB4DDLbcpipstBXCuLlVr6P9mUa066y5/BZ4u8aMTe3wNbWEgxa8nJz0WjL0+il9gR6l39qp2nIv8rab3Zi2W8UrwY8W0gXXQqndx3h4un1RDRdzrxXSiv28YBRxa6pI1hxOR+DmTsdB77L8J4v1kIm0tbRb5KShd/U58KBE2RZlsdKq0KlcKd5myZ4l3tQi3U5RJ3awaEIFebmCqxsrFCag0alIi9fjqtPQzp29vuL+ZlMTvyynHNOnXmvd10sX4RnGvVN9m8/TBr2mMugUmB7mvkWLGXMCtvB72dTkMktsLK1QpavQZWbg2fzfrSr41woHJmfdp2QK4dY/dVVemyewktuJbwk8imyLy/nvSm70Bj0uDTuw6h3B1G3lL8eT6JLvcTkHm04XG00o99qj0VmMnm5BpwCu9HZ735YXGTFcuTIYSJTZdg62GBhBnnZWZiV96ZFx674FM/aqD8Tudy+cJDDYXexcSqHLFeFzsabti81p0LR+h17gG/WRtB2xPu0dHla61cCig49S55epFwOFsu+6CKwayg+2XLbpChR7Ppuglh54W+EsV5E+XfFyQX9xReHixYUE6NB6NT/R7hFqxZnZ74h5kYWLSgNOpF8eZ9YOrGTwL6x+HSrSfDaoBInF48X0/YmmL6gxGXtGCneWREuVCWS8d4odHn5wmgoQ8nC/+SC+PyjX8X1O7lFC0qV7m6sCF7/s+hZCVF/yDwRZZLHPCdyl5gxaaWI+j++bs+fUdy5slA0sa8mBs89+69KhP+X9DqRp3kxfqNS7rIB5FSoHURV5T0cqvtQz79gOaDh1ALeX7Ceo3H300H9W+nyM4i6YEOLBkVLionMDHOrvz9Wz729m+WR7QuO3SlV5lSsHUQV5T0calShnl/BAilj/FY+mbqOvVdMUx6VND3nj0OjWtYoSyRSKsPcUonscUtZy4hb61Zh1rAuTo7Pf4vaP2Hu4EP9Os5o0n2oW8cf70etppGDs0bxyx9HSHjWFcnFSZtDyvFdnLFxxbOq9wsdRf7b5OZYWrwYv9EL0GmCMS+HkENX8KzkT12TfUKhB3ahEe60bFhyG26Lg04Xw23RhsCSCnv8XzLYPvMArT4ZxDNsGywRBnU2IYev4lXJjzomiwXvnNjFdaMVrZqV1FPI48QQkV8XPxeHFytk/G+VtI+lsXXo3MwPk6msF0Q+6VHHOe3oQVX/GgXbxYyh7N6eh51PS+qV5iQbAPEsersP78y/ho9dBpvGv8d3m86TW/Q2yT9WanOauux04uJuo3OqgpfiKH2rfID8gyVs+7YjxpwcDOYpLHi5K3NuvsyGsKkECjlKG6sSTPH0/AiDDq3BDAvli/3T6/VGzEv5OCDdvTTibsajc66Cp9lh+lb9COWYpWyb1gFDTg46uWDPqAZ8dLA6PxzfSG8nM+RWVjzTrqLnyWhAqxcoFOZ/Yx+w5IkMRoRM9gKNpNWk3rxJYrYSnypOnPqqCYPPBLFs80p6uKjJyRMYoxfQ7OU5lBu1gWMfB6KVKbGyKK3vuI68HA16ZMhkAmGUYW5pieVj9khK/plS6DTVxIXsZu+JW6SlpJNrDjZmMSz4LZp+i44zNzCa9VsPkJR+nd8W/EGGWxeGv9YI31ot6NGjgcnRSpKyJZfYs7vZe/I26Q/rhew681fdoP+io8xulsi234OJTotl19z1XFPWY+Dwzvj7NqJL75a4lVZbJSlztMnX2LMvmOjELFJVOhRmdtzcOYMbNaewccModPs2sPdiEqmXf2PugXT8e71Nz3q+NOrQnVY1CmXclZRBJfx8riH24ByGfjCLUHkjxsz4li/7uLB37lZw8qZ5oD0o7PGs6Y9TVgwZegMtBvQlsJYv3l4VSnWZsaQ4aYg5MJuhH87miqIxY2d8yxe9ndgzdytmzt40q28P5ra4VatFFdKJMWio1mcIHer4UqVyxf9sAnrJ86dJuczCUW/x/c40At+cyA/T3sM3Zgnrrrvg4d8QbwSWFbzwDXAm4WoGlrYt6d8nEN/q3riVl1qo/4SiK4OKkyouWLxd2UXUHjRPXH244lAfKSZ4VhC1O3wnok3uPfNVR1HZuZP4I0Pa6VzW5dzYK4Z5u4i6QxaIaw/qhVEXIcZ7VBB1O30vrpvcm7jyNVGtop/48eoLsVxRUpbo08SeqZ2EjXt7seDYww30RhG/oqewrNxAfH5YY3LzGTGsTmVRZfAfhZKVSMq+khtpilyidi/i1zvuvNSxLXUerDg0pl7iVL4Sh0bNKDj+NJIDZ5LJrt6eINsSWZooKS3GXCJ3LWZpqgcvd2xDrYf14k4oJ3VKHBo1pWBtWDYHd90g16wZzUwP3pZInoPsuPOsXRCMR5uONK3/MCOwkctnQ3F2qExTv4Jcb9rTBwlRZVO3fVCJpZ6TvBhKrNMUuSrO7NmKdS1f/AMLTjpNPxlMlMKcJu2CCm6Ou8CpOyl4tA3C8YnJ0yVlgTE3mzP7tmJduzp+9QvSRaefCiZaoaRJW5N6oQnj5K1M8po1wb/EV/5IyjYtKZEH2ZtUiSa16+H7MNOEMZzgXfk4enYg0CSdbnTIKVRqD9oFmSRhKOHVIZLSUWItj1abzPUIgWdFT6qZnJ965cQpFMoatPE3kpYQTkwGpF06Q0qyoGMLXxRmkJ0Rx8WQWxTvmQSS0qDTJnP9Gni5eVLVtF4cP4XSoiZt/A2kxocTnQYiLISr6ek069gCSznkZaURdf6qtKxe8s8ZteTGXiWtvCfeNas/OqHFePMMR/KVuLRuhlvmHeIiYjGSxvGDKahsO9C6shL0OcRfv8iVZF2RN5WURSXWaSot3KhSyw6jTIn1gxqpSdjDpgPZKKq/SguzWI5tXMFZtZG4iCQy1S1pWccemT6FY6vmsyFOSGGQMuh+vbBFyCx4eOyqJn43Gw/kYFGjL81lMRzdtIIQNSRGXeFuhjvtW5RHLnI5v20Rq46pHqUglEj+b2YW2PnUxlUuEJYPkytkcW7ddhIUdnTrWpPQEzvZuuc2ZtzgYloGtG9JLaWMu9HHWLtiA8myF26DqaQYlFjCdplSQTlZFgdOhoN9ZQzxF9m/9SBhideIUXpR3SKZa6k+9O9RD/3V3awJyaR6PWdunzzEpYwAxr7flBcrT4jkebhfLzIJPhmOzK4yhvgLD+pFBDFKL3yVKURm+PBajwCU8SdZvTUGlwa+ZF84RGicLf0m9MK1xB79JGWXHCsbWzLPHyJapcDDVsWZgzvZezqGxOhMXH1cuXvzJuW7vEG9iioubFhDuKwGAdbx7Dl8EauWYxkQILVQ/wUl1mmCOc5VG1DLXk18QipZ6Xdx6zKCsb0DUGSlkl+uIo37DKaugwwXL3fsbAUabR4agyevfdgXD2lbQRl1v17UtMslPjGdrPS7uHd9j7G9/JBn3SHf0Z2g3vfrhbWbFy7O1mhztWjybWj97jtI7ZTkeVHYe+BXz4O85JukZGWSKQ/gvc+G428vSMsWVPVrR9/WnpjjSlUPe5SGPDSaPGxrvcaILh5SEoH/iFJIbvA3jtd51vskZYP0/5a8EAQC2TNVRanK/veUTqcpkUgkEsm/kDQbJJFIJBLJM5I6TYlEIpFInpHUaUokEolE8oz+B6Ukz0dRwA99AAAAAElFTkSuQmCC\"\u003e\u003c/p\u003e\n \u003cp\u003ewhere \u0026beta; is the infection rate, \u0026delta; the infected cell death rate, \u003cem\u003ep\u003c/em\u003e the per-cell virus production rate, and \u003cem\u003ec\u003c/em\u003e the clearance rate. The ODE system was solved numerically using scipy.integrate.odeint (Python).\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec5\" class=\"Section3\"\u003e\n \u003ch2\u003e2.1.2 Stochastic intracellular dynamics.\u003c/h2\u003e\n \u003cp\u003eGiven the intrinsic noise of viral replication at tiny sizes, we used a stochastic simulation in accordance with Gillespie-style event-based techniques [13,14]. Infection, cell death, virion generation, and clearance are all reactions that happen with a probability that corresponds to their propensity. Exponential distributions were used to calculate waiting times. Poisson-tau leaping was also used to test faster approximations [15].\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec6\" class=\"Section3\"\u003e\n \u003ch2\u003e2.1.3 Population-level dynamics.\u003c/h2\u003e\n \u003cp\u003eWe expanded the model to a Susceptible\u0026ndash;Infected\u0026ndash;Recovered (SIR) system at the epidemiological scale [16,17]. The population model that was deterministic was:\u003c/p\u003e\n \u003cp\u003e\u003cimg 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\"\u003e\u003c/p\u003e\n \u003cp\u003ewhere \u003cem\u003eN\u003c/em\u003e is population size and \u0026gamma; is the recovery rate. Basic reproduction number (R0) and peak infection statistics were extracted to connect intracellular parameters with epidemic outcomes [18].\u003c/p\u003e\n \u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\n \u003ch2\u003e2.2 Module 2: Fast Stochastic Simulation with Mutation Effects\u003c/h2\u003e\n \u003cp\u003eScaling factors (1\u0026ndash;1.5\u0026times;) for \u0026beta; and p were introduced in order to investigate mutation-driven variations in viral infectivity and production. Stochastic Poisson approximations were used to simulate each mutant strain [15,19]. In order to represent genetic drift and selective advantage situations in viral evolution, variability was captured by averaging many simulations [20].\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\n \u003ch2\u003e2.3 Module 3: Multi-Strain Viral Dynamics with Immune Response and Treatment\u003c/h2\u003e\n \u003cp\u003eHost immunity and therapeutic intervention were incorporated into a two-strain stochastic model.\u003c/p\u003e\n \u003cul\u003e\n \u003cli\u003e\n \u003cp\u003e\u003cstrong\u003eImmune clearance.\u003c/strong\u003e An adaptive immune response was modeled as an increase in viral clearance rate (𝑐) after immune activation time [21].\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003e\u003cstrong\u003eTreatment effects.\u003c/strong\u003e Antiviral treatment was simulated as fractional reductions in \u0026beta; and \u003cem\u003ep\u003c/em\u003e after a specified onset time [22,23].\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003e\u003cstrong\u003eMutation effects.\u003c/strong\u003e The mutant strain was assigned enhanced infection and production rates, consistent with immune escape and fitness advantage mechanisms [24].\u003c/p\u003e\n \u003c/li\u003e\n \u003c/ul\u003e\n \u003cp\u003eInfection, death, production, and clearance events were sampled from Poisson distributions at each timestep, and parameters were continuously modified to account for treatment and immunological effects. This paradigm made it possible to evaluate the timing of interventions on peak viral levels and analyze competition between wildtype and mutant strains [25, 26].\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\n \u003ch2\u003e2.4 Module 4: Full Multi-Scale Viral Dynamics Analysis\u003c/h2\u003e\n \u003cp\u003eIn order to connect intracellular stochastic viral dynamics with population-level epidemic consequences, we employed a hybrid multi-scale modeling methodology in this module. A stochastic \u0026tau;-leaping approach was used to describe intracellular viral particle (V), infected cell generation (I), and target cell infection (T) [13,15,17]. The inclusion of distinct compartments for wildtype and mutant strains allowed for the measurement of infection rate (\u0026beta;), viral generation rate (p), and clearance rate (c) specific to each strain. Scaling the wildtype base parameters with a multiplicative factor (1.5\u0026times;) for the mutant strain allowed for the incorporation of mutation effects, which reflected increased replication and infectivity [4,23,24]. A time-dependent clearance function was used to boost viral particle clearance after an immunological onset threshold (day 3) in order to account for immune response dynamics [1,21]. Day 2 saw the start of antiviral therapy, which was modeled as a proportionate decrease in both \u0026beta; and p [25]. To capture the variability in viral load and infected cell peaks, ten stochastic realizations were simulated for each scenario. The results were presented as mean\u0026thinsp;\u0026plusmn;\u0026thinsp;standard deviation. Using parameters scaled by the average intracellular viral load of the mutant strain, the model was connected to a classical SIR framework at the population level [16,18]. An emergent fundamental reproduction number (R₀) was obtained by adjusting the effective population transmission coefficient (\u0026beta;_pop) to account for increased infectivity. Odeint from SciPy was used to solve the ODEs numerically [2,12]. Lastly, a sensitivity analysis was conducted over a range of \u0026beta; and p values, and the results were assessed in terms of the time to clearance and the maximum number of infected cells [6,7,26]. This method made it possible to measure the extent to which mutation-driven intracellular advantages lead to epidemic-level consequences.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\n \u003ch2\u003e2.5 Module 5: Integrated Multi-Scale Viral Dynamics Flow\u003c/h2\u003e\n \u003cp\u003eWe created an integrated multi-scale pipeline to expand Module 4, which methodically linked deterministic population-level epidemic trajectories with stochastic intracellular dynamics. There were six consecutive steps in this pipeline:\u003c/p\u003e\n \u003cul\u003e\n \u003cli\u003e\n \u003cp\u003eIntracellular viral dynamics are started with two competing strains (mutant and wildtype).\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003ePoisson sampling of infection, clearance, and viral production events is used in a stochastic simulation of intracellular viral dynamics over ten replicate runs [13,14].\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003ePeak viral loads for each strain are quantified and summarized as mean\u0026thinsp;\u0026plusmn;\u0026thinsp;standard deviation across simulations [9,20].\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eIntracellular results were propagated into a population-level SIR framework, where the transmission parameter (\u0026beta;_pop) was directly scaled by the mutant strain\u0026apos;s increased viral production rate [18,19].\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eCoupled ODEs computed with odeint are used for deterministic epidemic modeling at the host population level [2,16]. Time-to-peak, epidemic peak size, and R₀ were important outputs [11,22].\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eGlobal sensitivity analysis is used to evaluate the robustness of both within-host and between-host results by altering intracellular parameters (\u0026beta;, p) throughout biologically relevant ranges [5,23].\u003c/p\u003e\n \u003c/li\u003e\n \u003c/ul\u003e\n \u003cp\u003eThis integrated method aligns with current frameworks for multi-scale infectious illness modeling [3,6,10,19] by allowing a bottom-up perspective that links emergent epidemiological trends with molecular-scale alterations.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"3. Results","content":"\u003cp\u003eThe paradigm for multi-scale viral dynamics offered thorough insights into the intracellular and population-level behavior of both wildtype and mutant viral strains. Around day 38.2, the pandemic peaked at 3008 infected people, and the system generated a basic reproduction number (R₀) of 3.00 at baseline. The kinetics of intracellular infection changed significantly when mutation effects (mutation factor\u0026thinsp;=\u0026thinsp;1.5) were added. In the stochastic simulations, the mutant strain quickly grew to a significantly higher peak of 7299 infected cells at day 1.0, while the wildtype strain peaked at 2683 infected cells. The robustness of this divergence was validated by replicate stochastic simulations, which produced mutant peak values of 8069.1\u0026thinsp;\u0026plusmn;\u0026thinsp;1693.2 and wildtype peak values of 2680.0\u0026thinsp;\u0026plusmn;\u0026thinsp;1208.9. According to these results, the mutant strain continuously maintains greater infection loads in host cells. The effective reproduction number increased to R₀ = 4.50 at the population level when the intracellular mutant dynamics were coupled into an epidemic model. The epidemic trajectory was sharper, peaking at 24.2 days with 4431 infected individuals, which was significantly earlier and larger than the baseline epidemic peak. The way that small-scale mutational advantages result in larger-scale epidemic amplification is highlighted by this acceleration. Sensitivity testing of infection rate (β) and viral production rate (p) in addition to the fundamental intracellular and population analyses showed that increases in either parameter resulted in higher and earlier infection peaks, with β\u0026thinsp;=\u0026thinsp;0.0007 and p\u0026thinsp;=\u0026thinsp;100 producing the steepest and most severe trajectories when compared to lower parameter combinations respectively. Activated on day three, the immune response module resulted in higher clearance rates, which in some runs delayed progression and significantly decreased viral loads. The introduction of treatment on day two, which was modeled as a 50% drop in infection and production parameters, decreased the spread of both wildtype and mutant strains but did not completely eradicate infection; in all studied settings, the mutant strain remained dominant. These investigations collectively reveal a number of significant trends: Epidemic outcomes are highly sensitive to infection and production parameters, with relatively small increases driving disproportionately larger infection peaks; (i) mutation accelerates both infection peaks and epidemic spread; (ii) immune response and treatment reduce viral burdens but are insufficient to overcome mutant advantages; and (iv) stochastic intracellular dynamics reveal strong variability, but mutant strains consistently outcompete wildtype.\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eNew biological insights into how viral mutations affect infection outcomes at the intracellular and population levels are offered by the multi-scale stochastic and deterministic simulations that are provided here. Our results highlight the disproportionately enormous effects that even little changes in viral characteristics can have on disease dynamics. In particular, inserting a 1.5× mutation factor in viral production (p) and infection rate (β) reliably increased the severity of infection, leading to significantly higher peaks of infected cells in the host and faster epidemic propagation in the population model. These findings support the evolutionary advantage provided by mutations that increase viral fitness by demonstrating how seemingly insignificant genetic alterations at the molecular level can scale upward to alter the trajectory of epidemics. The robustness of mutant strain dominance is further demonstrated by our models' integration of immunological responses and treatment interventions. Although therapy started on day 2 and immune activation started on day 3 greatly decreased viral loads, these actions did not remove the competitive advantage of more contagious strains. This implies that although prompt interventions are still essential, they might not be enough to stop the faster dynamics of fitter viral variants unless they are paired with tactics that target mutation-driven amplification explicitly. Our multi-run stochastic simulations, which demonstrated significant variation in peak infection levels across multiple runs under identical settings, provide another important insight. This stochastic heterogeneity closely resembles clinical data where patients show different infection courses even though their exposure and risk variables are comparable. Because deterministic frameworks alone are unable to capture this real-world unpredictability, such variability highlights the significance of incorporating stochastic features in models of viral infection. When intracellular results were scaled to the population level, it became clear that mutation-driven effects directly translated into epidemic behavior. In addition to increasing the effective reproduction number (R₀), mutant strains also accelerated the onset of epidemic peaks and boosted the overall number of infected people. The idea that evolutionary advantages gained at the cellular level can spread to the population level, leading to more severe epidemic outcomes and making control efforts more difficult, is supported by these findings. Lastly, the sensitivity analyses show how important viral production (p) and infection rate (β) are in determining outbreak intensity and persistence. Even small adjustments to these factors can have a cascade effect on the dynamics of an epidemic, making them useful leverage points within the viral life cycle. We discovered the circumstances in which viral amplification is greatest by methodically altering these parameters, which may provide direction for therapeutic targeting and risk evaluation of new variations. When combined, these findings offer novel biological insights in the form of model-based predictions, going beyond simple computational exercises. Our paradigm illustrates how minor genetic alterations can have significant impacts on viral evolution and epidemic spread by connecting intracellular stochastic processes, immunological and therapeutic effects, and epidemic-scale transmission dynamics. In order to better predict the behavior of newly emerging viral variations and create more successful intervention tactics, these findings highlight the need to incorporate multi-scale and stochastic methodologies into infectious disease modeling.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch3\u003e\u003cstrong\u003eConflict of Interest - None\u003c/strong\u003e\u003c/h3\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eYuan, Y., \u0026amp; Allen, L. J. S. (2012). 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Antiviral resistance and the control of pandemic influenza: The roles of stochasticity, evolution and model details. \u003cem\u003eJournal of Theoretical Biology, 246\u003c/em\u003e(3), 458\u0026ndash;470. https://doi.org/10.1016/j.jtbi.2006.12.027\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"multi-scale modeling, stochastic viral dynamics, intracellular infection, viral mutation, multi-strain simulation, epidemic modeling, SIR model, immune response, treatment intervention, peak infection, population-level transmission","lastPublishedDoi":"10.21203/rs.3.rs-7728221/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7728221/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003ePredicting the course of epidemics and developing effective interventions depend on an understanding of how viral mutations affect infection dynamics at various biological scales. Here, we provide a thorough in silico investigation into the effects of viral mutations on infection progression by integrating population-level SIR modeling, immune response, multi-strain dynamics, and stochastic intracellular viral simulations. Stochastic simulations demonstrated that even slight mutation-induced increases in viral production or infectivity at the intracellular level resulted in significantly greater peaks in the number of infected cells. The amplification potential of minor genetic alterations was demonstrated by the fact that wildtype strains attained an average peak of around 2,680 infected cells, whereas mutant strains had an average peak of about 8,070 cells. The significance of random fluctuations in early infection dynamics was underscored by the models' capacity to capture underlying stochastic variability. It was discovered that mutations that accelerated intracellular infection directly translated into larger and faster epidemics when the intracellular viral load was coupled to a population-level SIR framework. In particular, mutant strains raised the effective reproduction number (R0) from 3.0 to 4.5, resulting in an earlier epidemic peak at about 24 days and a peak infected individual count of about 4,430. The robustness of these effects was further shown by sensitivity studies, which showed that infection peaks were extremely responsive to variations in viral generation and infectivity. All together, our multi-scale modeling methodology shows how minor cellular-level mutation-induced alterations can spread to affect epidemic outcomes at the population level. The significance of stochasticity in infection dynamics, the potential for early intervention measures to reduce intracellular viral amplification and epidemic development, and mechanistic insights into viral evolution are all highlighted by these findings. A strong computational tool for investigating the effects of viral mutations and guiding public health interventions is provided by this integrated platform.\u003c/p\u003e","manuscriptTitle":"From Virus to Population: Multi-Scale Stochastic Modeling Reveals Mutation-Driven Acceleration of Infection Dynamics","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-09-30 09:12:54","doi":"10.21203/rs.3.rs-7728221/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"34560ef6-8af1-4919-8b71-fdb8bc850648","owner":[],"postedDate":"September 30th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":55433300,"name":"Virology"},{"id":55433301,"name":"Epidemiology"},{"id":55433302,"name":"Statistical Epidemiology"},{"id":55433303,"name":"Bioinformatics"},{"id":55433304,"name":"Computational Biology"},{"id":55433305,"name":"Systems Biology"},{"id":55433306,"name":"Population Biology"}],"tags":[],"updatedAt":"2025-09-30T09:12:54+00:00","versionOfRecord":[],"versionCreatedAt":"2025-09-30 09:12:54","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7728221","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7728221","identity":"rs-7728221","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}