Fear-driven disease control: a two-host, one-parasite model with SI dynamics and behavioral change

Abstract

In this paper, we investigate the dynamics of two hosts and one parasite mathematical model with the fear effect and Susceptible-Infected SI disease. The parasite species reproduces by logistic growth law. There is a mutual fear between the first host and the second host. Infecting the second host with SI disease by transmission from the first host by contact or leaving a mark on its surroundings according to the Lotka-Volterra function. The model is studied theoretically, and its validity is studied numerically after obtaining of the local and the global equilibrium points. The parameter’s effect on the mathematical model is studied to determine which parameters cause damage and to set appropriate conditions to reduce their effect. This paper explores a novel disease control model where fear of a parasite drives behavioral changes in a two-host, and one-parasite system. The model utilizes the established SI framework to track disease spread alongside fear-induced modifications in host behavior, the disease was combated by controlling unstable balance points and making them stable.