Optimal control for dengue eradication program under the media awareness effect

Abstract

Abstract In this article, a mathematical model is proposed to assess the effects of media awareness on dengue eradication programs. First, the existence and local stability of equilibrium points are discussed using the concept of the basic reproduction number. Using the center-manifold theorem, it is shown that the proposed model always undergoes a forward bifurcation at the basic reproduction number equal to unity. It is observed that the high-intensity media awareness could reduce the size of the endemic equilibrium. Based on local sensitivity analysis, we identify the three most sensitive parameters, namely the natural death rate of mosquito (μ v ), infection rates (β h1, β v1), and hospitalization rate (η). Hence, control variables need to be introduced to increase/reduce these parameters. In this article, we use three different control variables, namely the media campaign, (u 1(t)), to reduce infection rates, additional hospitalization rate, (u 2(t)), and fumigation rate, (u 3(t)), to increase mosquitoes death rate. Pontryagin’s maximum principle is used to determine the optimal conditions. Some numerical simulations are performed to describe a possible scenario in the field. Cost effectiveness analysis is then conducted to determine the best strategy for the dengue eradication program. We conclude that a combination of media campaigns and fumigation is the most effective strategy to prevent a significant increase in the number of infected individuals.