An SIS infectious disease model with nonlinear incidence and disease awareness on complex networks

Social media holds a crucial position in mitigating the proliferation of infectious diseases, as the majority of individuals rely on media coverage to enhance their awareness of prevention measures. Based on the diversity of media coverage and the heterogeneity of the audience during the epidemic period, this paper establishes an SIS infectious diseases model on networks, employing a nonlinear incidence rate to capture the impact of media influence. By conducting a dynamic analysis of the model, the local stability and global stability of the disease-free equilibrium are demonstrated. Additionally, the unique existence, uniform persistence, and global attractiveness of the endemic equilibrium are verified. This article implements time-varying control on the self-isolation rate under media coverage, with the objective of managing the number of infected individuals, lowering contact rates, and minimizing promotional costs, while simultaneously achieving favorable promotional outcomes for the media. The optimal control solution for the model is derived using the Pontryagin’s Minimum Principle. The findings of the theoretical analysis are then validated through numerical simulation. The results indicate that the media coverage parameters do not influence the epidemic threshold, but they do impact the conditions for the persistence and attractiveness of the disease. Under optimal control, a balance is achieved between cost and infection scale. A moderate implementation rate can effectively curb the ongoing spread of the disease and significantly reduce the number of infections.