Impact of Behavioral Changes on Disease Spread: A Nonlinear Analysis of the S1S2IR Model

Abstract We outline and discuss here an expanded epidemiological model, called the S₁S₂IR model, which incorporates behavioral heterogeneity in the susceptible class. The model distinguishes the susceptible class into two classes: those with average behavior (S₁) and those practicing protective behavior (S₂), to reflect more realistically disease transmission dynamics. The dynamics are modeled by a nonlinear system of differential equations capturing behavioral switching, infection saturation phenomena, and key dynamics. We derive two basic reproduction numbers R_0₁ and R_0₁ as threshold parameters for characterizing the stability of equilibria. Local stability and global stability of DFE and EE are studied by the Jacobian matrix, Routh–Hurwitz conditions, and Lyapunov functions. Analytical conditions are obtained for the persistence and asymptotic stability of all equilibrium states. Numerical simulations are presented to gain understanding of the dynamic behavior of the system in both the endemic and disease-free scenarios. The results confirm that behavioral responses are a determining factor in long-term disease spread outcomes. This work highlights the importance of incorporating behavior-modified transmission into epidemic modeling and provides a theoretical framework for evaluating public health interventions. 2010 Mathematics Subject Classification: 92D30;34D23;34C23;37G10.