AN EPIDEMIC MODEL COUPLED WITH ENVIRONMENTAL LEVEL: EXPLORE THE IMPACT OF DISEASE AWARENESS ON DIRECT AND INDIRECT TRANSMISSION

To study the impact of disease awareness on infectious diseases with direct and indirect transmission, we develop a mathematical model by coupling the transmission dynamics at the population level and the environmental level. The basic reproduction number $R_0$ of the coupled model is calculated, and the existence and stability of the disease-free and endemic equilibrium are analyzed in detail. By using center manifold theory, it is verified that the model undergoes backward bifurcation under certain conditions. Numerical simulations verify our theoretical results and indicate that enhancing disease awareness can help reduce both the risk of direct and indirect disease transmission. Interestingly, increasing disease awareness decreases the backward regime of the bifurcation curve, thereby the $R_0$ interval in which the endemic equilibrium and the disease-free equilibrium showed bistability becomes smaller, and the $R_0$ interval in which the disease-free equilibrium showed global stability becomes greater. If the disease cannot be eliminated, the number of infected persons at the steady state decreases with the increase in disease awareness. The findings have certain reference values for the development of effective non-pharmaceutical intervention policies.