Dynamical Analysis of a Diphtheria Transmission Model with Epidemiological Data Fitting

Résumé

Abstract Diphtheria is a serious infectious disease caused by Corynebacterium diphtheriae, which affects the respiratory system and can lead to severe complications if not properly controlled. In this study, a compartmental deterministic epidemiological model governed by a system of nonlinear differential equations was formulated to investigate the transmission dynamics of diphtheria. Rigorous analysis of the model showed that the disease-free equilibrium was both locally and globally asymptotically stable when the basic reproduction number was less than unity, indicating that the spread of the disease could be effectively controlled under this condition. Real-life data on diphtheria were collected and fitted into the model in order to estimate key parameters. These estimated parameter values were then used to perform numerical simulations using MATLAB, which helped validate the analytical results obtained from the model. The simulations further explored the interaction dynamics of diphtheria in humans, including transmission patterns, disease progression, and its effects on the host population. Based on the findings, recommendations were made to healthcare policymakers on effective strategies for controlling and reducing the spread of the disease and minimizing its public health burden. Keywords: Diphtheria; Data fitting; Sensitivity analysis; Basic reproduction number; Numerical simulation.

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