Bifurcation analysis and optimal control of discrete SIR model for COVID-19

Abstract

Our research focuses on studying a COVID-19 SIR model for discrete cases, incorporating bi-linear phenomena and a constant rate of recovery. We have interested in analyzing the conditions for the existence of disease-free equilibrium and local equilibrium in this model. Additionally, we are investigating the stability of several bifurcations, including saddle–node bifurcations, flip bifurcations, 1:1 resonances, and Neimark-Sacker bifurcations. These bifurcations provide insights into the behavior and dynamics of the system as specific parameters change. We propose a vaccine response rate to introduce a control variable for the SIR system. This variable represents the rate at which individuals receive vaccinations, which can affect the spread of the disease. Finally, demonstrate an epidemic model based on vaccination control with social awareness, using the results and insights obtained from our analysis to showcase the effectiveness of the proposed control strategy in mitigating the spread of COVID-19. In our research, we also employ Pontryagin’s maximum principle to solve the system. By applying this principle, we can determine the optimal control strategy that minimizes the spread of the disease or achieves other desired objectives. We have conducted a comprehensive analysis of the COVID-19 SIR model with a focus on bifurcations, control strategies, and social awareness about the impact of vaccination. Such research contributes to our understanding of the dynamics of infectious diseases and provides valuable insights for controlling epidemics.