A mathematical model to estimate transmission dynamics of COVID-19 is developed. A real data of confirmed cases for Ethiopia is used for parameter estimation via model fitting. Results showed that, the diseases free and endemic equilibrium points are found to be locally and globally asymptotically stable for R o <1 and R o >1 respectively. The basic reproduction number is R o =1.5085. Optimal control analysis also showed that, combination of optimal preventive strategies such as public health education, personal protective measures and treatment of hospitalized cases are effective to significantly decrease the number of COVID-19 cases in different compartments of the model.

Analysis of mathematical models designed for COVID-19 results in several important outputs that may help stakeholders to answer disease control policy questions. A mathematical model for COVID-19 is developed and equilibrium points are shown to be locally and globally stable. Sensitivity analysis of the basic reproductive number (R 0 ) showed that the rate of transmission from asymptomatically infected cases to susceptible cases is the most sensitive parameter. Numerical simulation indicated that a 10% reduction of R 0 by reducing the most sensitive parameter results in a 24% reduction of the size of exposed cases. Optimal control analysis revealed that the optimal practice of combining all three (public health education, personal protective measure, and treating COVID-19 patients) intervention strategies or combination of any two of them leads to the required mitigation of transmission of the pandemic.

Robust finite difference method is introduced in order to solve singularly perturbed two parametric parabolic convection-diffusion problems. In order to discretize the solution domain, Micken’s type discretization on a uniform mesh is applied and then followed by the fitted operator approach. The convergence of the method is established and observed to be first-order convergent, but it is accelerated by Richardson extrapolation. To validate the applicability of the proposed method, some numerical examples are considered and observed that the numerical results confirm the agreement of the method with the theoretical results effectively. Furthermore, the method is convergent regardless of perturbation parameter and produces more accurate solution than the standard methods for solving singularly perturbed parabolic problems.

We consider a SEAIR epidemic model with Atangana–Baleanu fractional-order derivative. We approximate the solution of the model using the numerical scheme developed by Toufic and Atangana. The numerical simulation corresponding to several fractional orders shows that, as the fractional order reduces from 1, the spread of the endemic grows slower. Optimal control analysis and simulation show that the control strategy designed is operative in reducing the number of cases in different compartments. Moreover, simulating the optimal profile revealed that reducing the fractional-order from 1 leads to the need for quick starting of the application of the designed control strategy at the maximum possible level and maintaining it for the majority of the period of the pandemic.

In this paper, exponentially fitted finite difference method for solving singularly perturbed delay differential equation with integral boundary condition is considered. To treat the integral boundary condition, Simpson's rule is applied. The stability and parameter uniform convergence of the proposed method are proved. To validate the applicability of the scheme, two model problems are considered for numerical experimentation and solved for different values of the perturbation parameter,  and mesh size, .h The numerical results are tabulated in terms of maximum absolute errors and rate of convergence and it is observed that the present method is more accurate and  -uniformly convergent for h   where the classical numerical methods fails to give good result and it also improves the results of the methods existing in the literature.