Dynamical behavior of SIRS model incorporating government action and public response in presence of deterministic and fluctuating environments

Abstract

In the present article, global characteristics of a generalized SIRS (susceptible–infected–recovered–susceptible) epidemic model have been investigated incorporating government policy, public response and social behavioral reaction. The effects of environmental fluctuations and time-dependent control strategies on the disease dynamics have also been analyzed. In the case of deterministic model, it is shown that the disease invades in this system when the basic reproduction number (R0) is greater than 1, whereas the dynamics of the stochastic model can be controlled by its associated basic reproduction number R̃s. Specifically, this work emphasizes the importance of nonlinear dynamic analysis of epidemic modeling, as well as the significant impact of social and government actions on disease dynamics. Numerical figure depicts that the governmental action plays a crucial role to control an epidemic situation, and the system turns out to be disease-free sooner if the government takes action at an early stage during a disease outbreak. Furthermore, one of the most key developments is that random fluctuations can prevent disease outbreaks, which can lead to the development of useful control techniques to restrict disease dynamics. The governmental actions and the clinical treatment are considered to be the effective control pair in this model, and it can be observed that the simultaneous implementation of the control strategies significantly reduces the disease burden.