Optimal control analysis of a COVID-19 and Tuberculosis (TB) co-infection model with an imperfect vaccine for COVID-19

Abstract

This paper presents a co-infection mathematical model of COVID-19 and TB to study their synergistic dynamics. We first investigated the single infection models of each disease and then the co-infection dynamics of the two diseases. Indeed, we calculated the basic reproduction number of each model, and then we studied the existence and the stability of the equilibrium points. We subsequently proved that the TB only infection model and the co-infection model exhibit backward and forward bifurcations. In addition, we performed a sensitivity analysis of the basic reproduction numbers to determine which parameters influence them the most. Furthermore, we applied Pontryagin’s maximum principle to our co-infection model to assess the impact of the use of an imperfect vaccine for COVID-19, taken as an optimal control strategy. Finally, we presented the results of the numerical simulations to support the theoretical findings.

Developing computationally efficient optimal control strategies to eradicate Rubella disease

“…It allows them to assess the effectiveness of different strategies, explore tradeoffs, and guide decision-making processes. The application of optimal control analysis to epidemic models has proven successful in addressing various infectious diseases, such as influenza, HIV/AIDS, tuberculosis, and Covid-19 [26,33,34]. It provides valuable insights into the dynamics of epidemics and helps inform public health policies to mitigate the spread of diseases, reduce healthcare burdens, and protect vulnerable populations.…”

A Model of Tuberculosis and Diabetes Co-Infection with Optimal Control

“…These investigations have delved into the application of optimal control strategies for mitigating multidrug-resistant TB (MDR-TB) and extensively drug-resistant TB (XDR-TB) [32,51]. Furthermore, analyses employing optimal control have been suggested for co-infection models, incorporating measures such as TB sensitization, dietary sensitization, and TB vaccination [12]. The studies underscore the significance of concurrently addressing TB and diabetes for effective outcomes, emphasizing the necessity for comprehensive strategies in managing co-infection scenarios [12,4].…”