Mathematical Modeling for Exploring the Influence of Infectious Diseases
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Date
2025-06-14
Authors
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Journal ISSN
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Publisher
Mohamed Boudiaf University of M'sila
Abstract
This thesis explores the role of mathematical modeling in understanding the
spread of infectious diseases, with a focus on individuals with chronic conditions. It
builds on classical models SI, SIS, SIR, SIRS and develops an extended SECIR model that
accounts for chronic health status. The study shows how chronic diseases can increase
infection risk and accelerate epidemic spread among vulnerable populations. It analyzes
key indicators like the basic reproduction number Rp, considering social, environmental,
and health factors. The findings highlight the importance of using mathematical models
to guide public health policies, especially in vaccination planning and prioritizing care for
high-risk groups. The thesis underscores the value of collaboration between
mathematicians and epidemiologists for effective epidemic preparedness.
Description
Keywords
Mathematical modeling, MEDICINE::Microbiology, immunology, infectious diseases::Infectious diseases, Chronic diseases, Epidemiological models, Equilibrium Points, Stability of Equilibrium Points, Basic Reproduction Number, Fixed Point Theorem