Mathematical Modeling and Analysis of TB and COVID-19 Coinfection

Abstract

Tuberculosis (TB) and coronavirus (COVID-19) are both infectious diseases that globally continue affecting millions of people every year. They have similar symptoms such as cough, fever, and difficulty breathing but differ in incubation periods. This paper introduces a mathematical model for the transmission dynamics of TB and COVID-19 coinfection using a system of nonlinear ordinary differential equations. The well-posedness of the proposed coinfection model is then analytically studied by showing properties such as the existence, boundedness, and positivity of the solutions. The stability analysis of the equilibrium points of submodels is also discussed separately after computing the basic reproduction numbers. In each case, the disease-free equilibrium points of the submodels are proved to be both locally and globally stable if the reproduction numbers are less than unity. Besides, the coinfection disease-free equilibrium point is proved to be conditionally stable. The sensitivity and bifurcation analysis are also studied. Different simulation cases were performed to supplement the analytical results.

A mathematical model for the co-dynamics of COVID-19 and tuberculosis

“… We assume that people with COVID-19 are susceptible to infection with TB and vice versa based on several case reports on the co-infection of the two diseases [25] , [35] . Co-infected people cannot recover simultaneously from both infections; they can only recover from one disease at a time [41] , [42] . For instance, the recovery rate of co-infected latent TB and COVID-19 individuals is given as such that when the person recovers from tuberculosis, they move to the infected COVID-19 population at the rate .…”

“…Co-infected people cannot recover simultaneously from both infections; they can only recover from one disease at a time [41] , [42] . For instance, the recovery rate of co-infected latent TB and COVID-19 individuals is given as such that when the person recovers from tuberculosis, they move to the infected COVID-19 population at the rate .…”

Mathematical modeling and optimal control of SARS-CoV-2 and tuberculosis co-infection: a case study of Indonesia

“…( 2020 ) and Mishra et al. ( 2021 ). Co-existence of TB and SARS-CoV-2 is almost evident due to the their worldwide geographic overlap (Khurana and Aggarwal 2020 ).…”

The impact of COVID-19 on a Malaria dominated region: A mathematical analysis and simulations

“…For example, see [22] , [23] , [24] , [25] , [26] , [27] , [28] , [29] , [30] , [31] , [32] , [33] , [34] and the references therein. To better understand the dynamics of co-infection diseases, some studies have been developed (see [21] , [35] , [36] , [4] , [37] ). However, more work is still needed to understand the co-infection of the recently discovered pandemic disease COVID-19 with other diseases.…”