SEIR Mathematical Model for Influenza-Corona Co-Infection with Treatment and Hospitalization Compartments and Optimal Control Strategies

• Published in: Computer modeling in engineering & sciences Vol. 142; no. 2; pp. 1899 - 1931
• Main Authors: McKinney, Brett, Imran, Muhammad, Butt, Azhar Iqbal Kashif
• Format: Journal Article
• Language: English
• Published: Henderson Tech Science Press 2025
• Subjects: Compartments; Disease control; Effectiveness; Health services; Infections; Influenza; Mathematical models; Optimal control; Parameter identification; Parameter sensitivity; Public health; Sensitivity analysis
• ISSN: 1526-1506; 1526-1492; 1526-1506
• DOI: 10.32604/cmes.2024.059552

The co-infection of corona and influenza viruses has emerged as a significant threat to global public health due to their shared modes of transmission and overlapping clinical symptoms. This article presents a novel mathematical model that addresses the dynamics of this co-infection by extending the SEIR (Susceptible-Exposed-Infectious-Recovered) framework to incorporate treatment and hospitalization compartments. The population is divided into eight compartments, with infectious individuals further categorized into influenza infectious, corona infectious, and co-infection cases. The proposed mathematical model is constrained to adhere to fundamental epidemiological properties, such as non-negativity and boundedness within a feasible region. Additionally, the model is demonstrated to be well-posed with a unique solution. Equilibrium points, including the disease-free and endemic equilibria, are identified, and various properties related to these equilibrium points, such as the basic reproduction number, are determined. Local and global sensitivity analyses are performed to identify the parameters that highly influence disease dynamics and the reproduction number. Knowing the most influential parameters is crucial for understanding their impact on the co-infection’s spread and severity. Furthermore, an optimal control problem is defined to minimize disease transmission and to control strategy costs. The purpose of our study is to identify the most effective (optimal) control strategies for mitigating the spread of the co-infection with minimum cost of the controls. The results illustrate the effectiveness of the implemented control strategies in managing the co-infection’s impact on the population’s health. This mathematical modeling and control strategy framework provides valuable tools for understanding and combating the dual threat of corona and influenza co-infection, helping public health authorities and policymakers make informed decisions in the face of these intertwined epidemics.