Spatio-Temporal Patterns and Hopf Bifurcation in a Two-Delayed SIR Model with Diffusion and Network Connectivity

Within the framework of a random network, where the network architecture specifies the directional flow between nodes, this study delves into the SIR (Susceptible-Infected-Recovered) model. We incorporate two distinct time delays into the model: one representing the recovery period of infected individuals and the other the incubation time for susceptibles to become infectious. The model is developed using continuous-time and discrete-space equations that account for dual delays within the diffusion network. By employing the delay as a bifurcation parameter, we derive the essential conditions for the onset of Hopf bifurcation. The stability of this Hopf bifurcation is then scrutinized utilizing the central manifold theory. Our numerical simulations confirm that the stability features associated with the Hopf bifurcation can trigger disease outbreaks. Furthermore, our research reveals that the connection probability within the network significantly alters the spatio-temporal dynamics of the epidemic spread. This insight underscores the importance of network connectivity in influencing epidemic patterns and has implications for public health interventions and disease control strategies. Supplementary Material File (delay sirs2 check.pdf) - Download - 2.48 MB Information & Authors Information Version history Copyright This work is licensed under a Non Exclusive No Reuse License.

Authors Metrics & Citations Metrics Article Usage 256views 158downloads Citations Download citation Wenjie Yang, Qianqian Zheng, Jianwei Shen, et al. Spatio-Temporal Patterns and Hopf Bifurcation in a Two-Delayed SIR Model with Diffusion and Network Connectivity. Authorea. 05 March 2025. DOI: https://doi.org/10.22541/au.174116533.37760617/v1 DOI: https://doi.org/10.22541/au.174116533.37760617/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu.