Prevention of dengue virus transmission: insights from host-vector mathematical model

Dengue fever is caused by the dengue virus transmitted by female Aedes Aegypti. The spread of dengue fever remains a critical public health issue. Dengue fever is a cycle between humans and mosquitoes. A high number of infected humans causes a high number of infected mosquitoes, and vice versa. Therefore, in this study, we develop a new mathematical model that considers the host for the human population and the vector for the mosquito population. This study focuses on capturing the fundamental dynamics of dengue virus transmission using a widely understandable host-vector model. The analysis is divided into two models: one without control and one with control. In the mathematical model without control, we obtain the basic reproduction number, which is determined using the next-generation matrix. We use the basic reproduction number to analyze the local stability of the disease-free equilibrium and the Routh-Hurwitz criterion for the endemic equilibrium. Additionally, we employ LaSalle's invariance principle and Lyapunov functions to analyze the global stability of both equilibriums. Moreover, we predict the virus spread through a sensitivity analysis of the key parameters that influence the basic reproduction number. We extend the model with control, which promotes for a thorough understanding of the effects of a single-control strategy in depth. Following this analysis, a preventive control strategy using Pontryagin's Maximum Principle is developed to minimize contact between the host and vector, ultimately reducing the spread of the dengue virus. Then, these strategies are numerically solved to investigate the control efforts required to reduce the number of infected classes.