Modeling the dynamics of co-infection between COVID-19 and tuberculosis with quarantine strategies: A mathematical approach

Abstract

As a result of COVID-19 and tuberculosis (TB) co-infection, public health is at risk. Various organs in the body may be affected by a co-infection of COVID-19 and TB. It has been shown that COVID-19 and TB co-infect humans through a bilinear incidence rate. An analysis of the efficacy of quarantine compartments for individuals with COVID-19 and who are co-infected with COVID-19 and TB is conducted using a mathematical model of COVID-19 and TB co-infection. To model the dynamics of COVID-19 and TB co-infection, we first illustrate the disease dynamics schematically and then apply the law of mass action to obtain nonlinear ordinary differential equations. Analysis of the boundedness, positivity, and equilibrium points of the system has been performed. On the basis of the next-generation matrix (NGM) technique, the reproduction number is calculated to determine the stability of the free equilibrium point. Whenever R0 < 1, the equilibrium points that are disease-free are locally asymptotically stable, but not globally. Numerical simulation shows that the use of quarantine strategies, θ1 (quarantine rates for people suffering from COVID-19) and ϕ (quarantine rates for co-infected individuals), was found to be impactful in the control of TB infection and TB–COVID-19 co-infection spread in the population if the values of those coefficients were increased. To prevent the spread of infection in the community, it is important that government stakeholders focus on the key criteria of quarantine for COVID-19 and TB co-infection.