Study of Some Differential Dynamic Systems Linked to the Spread of Epidemics

Abstract

This thesis introduces and investigates several innovative models to analyze and comprehend the transmission dynamics of mosquito-borne infectious diseases, including malaria, dengue fever, and cutaneous leishmaniasis. It provides a comprehensive analysis of the spread of these diseases through numerical simulations, utilizing recent health data from multiple countries. Furthermore, the study examines solutions' existence, uniqueness, and stability, alongside an exploration of the basic reproduction number, equilibrium points, and their stability properties. The numerical simulations reveal a direct correlation between transmission rates and the number of infected individuals, underscoring the urgent need to implement effective treatment protocols.