Optimal control analysis for the coinfection of COVID-19 and TB

Abstract

The COVID-19 pandemic continues to clame the lives of many people globally and controlling the disease has became the most challenging part of the modern health care system. Tuberculosis (TB) is also a major global health threat affecting millions of people every year. In this study, we extended the deterministic mathematical model to provide insight for the coinfection of COVID-19 and TB into an optimal control problem. The validity of the coinfection model is qualitatively studied by showing the well-posedness and positivity of the solutions. The analytical computations on the impacts of the disease revealed that an increase in infected individuals with TB has a positive impact on the spread of COVID-19 while under some conditions, an increase in the number of COVID-19 cases has a positive impact on the spread of TB disease. We add four control measures in the deterministic model such as: the prevention effort against TB, prevention techniques against COVID-19, treatments for TB infections and medical care for COVID-19 infection to optimally manage the diseases. The extended optimal control problem is analyzed with the help of Pontryagin’s Minimum Principle. The existence and uniqueness of optimal control are proved. We fitted the parameter values of our proposed model with collected epidemiological data using a modified combination of the Bayesian and least square estimation technique. Different simulation cases were performed to compare the analytical results and to identify the most appropriate control intervention strategies. The simulation results show that the prevalence of the coinfection reduced when all the four control measures were concurrently implemented.

Keywords:

• TB
• COVID-19
• coinfection
• optimal control
• Pontryagin’s Minimum Principle

Acknowledgments

The first author acknowledges Adama Science and Technology University under grant number ASTU/SP-R/120/21, and the Simon’s foundation fellowship through Research and Graduate studies in mathematics and its applications (RGSMA), Botswanan International University of Science and Technology (BIUST), for their financial support.

Availability of data and materials

The data used to support the findings of this study are included within the sections of the article and available in Johns Hopkins University (2022) and S. T. Partnership (2020).

Declaration of competing interest

The authors would declare that they have no competing interests that could appeared to influence this work.