Dynamics of a Vector-Host SIR-SI Model in Dengue Transmission

Abstract

Dengue fever is a major health problem, especially in tropical and subtropical areas, affect- ing around 50 countries. The disease is mainly spread by Aedes mosquitoes, with Aedes aegypti being the most important carrier. Urbanization, climate change, and population movement make it spread more easily. Dengue symptoms can range from mild fever to se- vere hemorrhagic fever, which can be fatal. To control the disease, effective strategies are needed, and epidemiological models are crucial for understanding disease spread, testing interventions, and predicting outbreaks. In this project, we will create a model that describes the relationship between humans and mosquitoes using a susceptible-infected-recovered (SIR) model for people and a susceptible- infected (SI) model for mosquitoes. The goal is to understand how these two groups in- teract and use this information to improve control measures. We will calculate the basic reproduction number (Ro) using the Next Generation Matrix method to determine whether the disease will spread (Ro > 1) or fade out (Ro < 1). We will also use stability analysis with the Lyapunov function to check these results. Furthermore, we will run simulations in MATLAB to test the model and explore the effects of control measures like mosquito population control, vaccination, and quarantine. By doing sensitivity analysis, we will identify the most important factors affecting disease spread and help prioritize the best in- terventions. The project aims to provide useful insights into how dengue spreads and guide effective ways to control it.