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.

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.

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n this paper, we have implemented the finite element method for the numerical solution of a boundary and initial value problems, mainly on solving the one and two-dimensional advection-diffusion equation with constant parameters. In doing so, the basic idea is to first rewrite the problem as a variational equation, and then seek a solution approximation from the space of continuous piece-wise linear’s. This discretization procedure results in a linear system that can be solved by using a numerical algorithm for systems of these equations. The techniques are based on the finite element approximations using Galerkin’s method in space resulting system of the first order ODE’s and then solving this first order ODE’s using backward Euler descritization in time. For the two-dimensional problems, we use the ODE solver ODE15I to descritize time. The validity of the numerical model is verified using differenttest examples. The computed results showed that the use of the current method is very applicable for the solution of the advection-diffusion equation.