Study of Some Differential Dynamic Systems Linked to the Spread of Epidemics
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Date
2025-06-15
Journal Title
Journal ISSN
Volume Title
Publisher
University of Mohamed Boudiaf, Faculty of Mathematics and Computer Science, Mathematics Department
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.
Description
Keywords
Mathematical modeling, MEDICINE::Microbiology, immunology, infectious diseases, population dynamics, malaria, dengue fever, cutaneous leishmaniasis, existence, uniqueness, basic reproduction number, equilibrium points, stability analysis, numerical simulations, estimation parameters, health data analysis, and treatment protocols