Nonlinear state-dependent pulse control for an SIRS epidemic model with varying size and its application to the transmission of brucellosis

College of Mathematics and System Science, Xinjiang University, Urumqi 830017, P.R. China.

^* Corresponding author: lfnie@163.com

Received: 15 October 2020
Accepted: 16 October 2021

Abstract

As the disease spreads, it will inevitably cause important damage to the life and health of the population, resulting in changes in the population quantity. In addition, in some economically underdeveloped areas, limited medical resources will also have an important impact on the prevention and control of diseases. Based on these, a susceptible-infected-recovered-susceptible (SIRS) epidemic model is established, where state-dependent pulse control strategy, varying total population and limited medical resources are introduced. By using the qualitative theory of ordinary differential equation, differential inequality techniques, Poincaré map, and other methods, some sufficient conditions of the existence and orbital asymptotical stability of positive order-1 or order-2 periodic solution are obtained in various situations. Theoretical results imply that the proportion of infected class can be controlled at a desired low level for a long time and disease will not break out among population. Finally, based on realistic parameters of brucellosis in ruminants, numerical simulations have been performed to expalin/extend our analytical results and the feasibility of the state-dependent feedback control strategy.