Study of a SIQR Model with Optimal Control Techniques: A Mathematical Approach

The ongoing COVID-19 pandemic has drawn attention of the international community and reignited the discussion about our capacity to control outbreaks of epidemics and pandemics. In this article, a SIQR deterministic model with non-linear incidence function for an infectious disease is formulated and analyzed. The equilibria and the basic reproduction number (R0) of the model are found. The local and global stability of different equilibria of the model is discussed. Further, considering screening and treatment as controls, this model is extended to optimal control model and is analyzed by Pontryagin’s Maximum Principle. Moreover, we performed numerical analysis to illustrate our theoretical findings. Our study suggests that use of both control interventions not only reduce the severity of disease burden but also minimize the economic burden occurred due to these interventions.