Mathematical Modeling with Two Strains to Investigate Evolution of COVID-19 from Computational and Theoretical Perspectives

The respiratory disease COVID-19 is brought on by a mutagenic {ribonucleic acid (RNA)} virus. Variants with various traits that could potentially impact transmissibility started to appear globally in December 2020. We develop and examine a computational model of two-strain COVID-19 transmission behaviors in order to deal with this novel aspect of the disease. After a theoretical analysis, enough criteria are derived for the stability of the model's equilibrium. The model contains single-strain 1 and variant 2 endemic equilibria as well as disease-free and endemic equilibria. The global stability of the model equilibrium is demonstrated using the Lyapunov function. For each strain, we separately compute the basic reproductive numbers $\mathscr{R}_{01} <1$, and $\mathscr{R}_{02}<1$. To determine the realistic values of the model parameters, the actual data from South Africa for the period of three months, are taken into consideration.Sensitivity study employing the {partial rank correlation coefficient technique (PRCC)} to look into the key variables that affect $\mathscr{R}_{01} <1$, or $\mathscr{R}_{02}<1$ decrease or increase. We show the numerical simulation of the model using {non-standard finite difference scheme (NSFDS)} and Caputo fractional derivative for distinct non-integer order. The world health organizations (WHO) recommends {standard operating procedures (SOPs)} to minimize infection in the population. Based on these recommendations, some graphical results for the model with sensitive parameters are provided.