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.

In this paper, we apply optimal control theory to a novel coronavirus transmission model given by a system of non-linear ordinary differential equations. Optimal control strategies are obtained by minimizing the number of exposed and infected population considering the cost of implementation. The existence of optimal controls and characterization is established using Pontryagin's Maximum Principle. An expression for the basic reproduction number is derived in terms of control variables. Then the sensitivity of basic reproduction number with respect to model parameters is also analysed. Numerical simulation results demonstrated good agreement with our analytical results. Finally, the findings of this study shows that comprehensive impacts of prevention, intensive medical care and surface disinfection strategies outperform in reducing the disease epidemic with optimum implementation cost.

A mathematical model for the transmission dynamics of Coronavirus diseases (COVID-19) is proposed using a system of nonlinear ordinary differential equations by incorporating self protection behavior changes in the population. The disease free equilibrium point is computed, and both the local and global stability analysis was performed. The basic reproduction number ( ) of the model is computed using the method of next generation matrix. The disease free equilibrium point is locally asymptotically and globally stable under certain conditions. Based on the available data, the unknown model parameters are estimated using a combination of least square and Bayesian estimation methods for different countries. The forward sensitivity index is applied to determine and identify the key model parameters for the spread of disease dynamics. The sensitive parameters for the spread of the virus vary from country to country. We found out that the reproduction number depends mostly on the infection rates, the threshold value of the force of infection for a population, the recovery rates, and the virus decay rate in the environment. It illustrates that control of the effective transmission rate (recommended human behavioral change towards self-protective measures) is essential to stop the spreading of the virus. Numerical simulations of the model were performed to supplement and verify the effectiveness of the analytical findings.

A mathematical model for the transmission dynamics of Coronavirus diseases (COVID-19) is proposed by incorporating self-protection behavior changes in the population. The disease-free equilibrium point is computed and its stability analysis is studied. The basic reproduction number(R 0 ) of the model is computed and the disease-free equilibrium point is locally and globally stable for R 0<1 and unstable for R 0 >1. Based on the available data the unknown model parameters are estimated using a combination of least square and Bayesian estimation methods for different countries. Using forward sensitivity index the model parameters are carried out to determine and identify the key factors for the spread of disease dynamics. From country to country the sensitive parameters for the spread of the virus varies. It is found out that the reproduction number depends mostly on the infection rates, the threshold value of the force of infection for a population, the recovery rates, and the virus decay rate in the environment. It is also demonstrated that control of the effective transmission rate (recommended human behavioral change towards self-protective measures) is essential to stop the spreading of the virus. Numerical simulations also show that the virus transmission dynamics depend mostly on those sensitive parameters.