Affiliation:
1. Laboratory of Pure and Applied Mathematics Mohamed Boudiaf University of M'sila M'sila 28000 Algeria
2. Laboratory of Mathematics and Their Interactions Abdelhafid Boussouf University Center of Mila Mila 43000 Algeria
3. Laboratory of Pure and Applied Mathematics University of Mostaganem Mostaganem 27000 Algeria
Abstract
AbstractThis paper presents an in‐depth analysis of a hybrid mathematical model, the fractional SECIR model, designed to explore the impact of infectious diseases, with particular emphasis on their effect on individuals with chronic conditions. The study delves into the existence and uniqueness of solutions for the proposed model, yielding several stability results based on parameters that adhere to specific conditions to mitigate pandemic occurrences. The model parameters are estimated using data reported by the Algerian health authorities in recent years, facilitating the application of the model to the Algerian context. The findings derived from the application of this mathematical compartmental model indicate that the basic reproduction number for certain infectious diseases in Algeria (Tuberculosis and COVID‐19) is less than one. This observation suggests the potential for disease eradication or effective management through a combination of targeted interventions including vaccination, high‐quality treatment, and precise isolation measures.