Mathematical modelling and analysis of COVID-19 and tuberculosis transmission dynamics
Ram Singh, Attiq ul Rehman, Tanveer Ahmed, Khalil Ahmad, Shubham Mahajan, Amit Kant Pandit, Laith Abualigah, Amir H. Gandomi
Abstract
In this paper, a mathematical model for assessing the impact of COVID-19 on tuberculosis disease is proposed and analysed. There are pieces of evidence that patients with Tuberculosis (TB) have more chances of developing the SARS-CoV-2 infection. The mathematical model is qualitatively and quantitatively analysed by using the theory of stability analysis. The dynamic system shows endemic equilibrium point which is stable when R0<1 and unstable when R0>1. The global stability of the endemic point is analysed by constructing the Lyapunov function. The dynamic stability also exhibits bifurcation behaviour. The optimal control theory is used to find an optimal solution to the problem in the mathematical model. The sensitivity analysis is performed to clarify the effective parameters which affect the reproduction number the most. Numerical simulation is carried out to assess the effect of various biological parameters in the dynamic of both tuberculosis and COVID-19 classes. Our simulation results show that the COVID-19 and TB infections can be mitigated by controlling the transmission rate γ.