Mathematical Analysis of SIR Epidemic Model with Piecewise Infection Rate and Control Strategies (Journal of Nonlinear Modeling and Analysis, 2024)
The limitation of contact between susceptible and infected individuals plays an important role in decreasing the transmission of infectiousdiseases. Prevention and control strategies contribute to minimizing the transmission rate. In this paper, we propose SIR epidemic model with delayedcontrol strategies, in which delay describes the response and effect time. Westudy the dynamic properties of the epidemic model from three aspects: steadystates, stability and bifurcation. By eliminating the existence of limit cycles,we establish the global stability of the endemic equilibrium, when the delay isignored. Further, we find that the delayed effect on the infection rate does notaffect the stability of the disease-free equilibrium, but it can destabilize theendemic equilibrium and bring Hopf bifurcation. Theoretical results show thatthe prevention and control strategies can effectively reduce the final numberof infected individuals in the population. Numerical results corroborate thetheoretical ones.
Keywords: Epidemic model; prevention and control strategy; piecewise infection rate; Hopf bifurcation.