Numerical Analysis of Deterministic and Stochastic Model of COVID-19 Co-infection with Influenza

The dynamics of co-infection model of SARS-Cov-2 and influenza is presented in this paper. A detailed analysis is conducted on the possible effects of the influenza vaccination alone as well as the combined effect of both vaccinations on the co-infection dynamics. The two diseases' basic reproduction numbers utilizing the next-generation matrix method.Endemic equilibrium point (EEP), and disease free equilibrium points (DFEP) are calculated for deterministic model. The global stability of the model equilibrium is demonstrated using the Lyapunov function function, and the local stability is discussed for deterministic as well as stochastic. There are supplied simulations to highlights the theoretical outcomes of the model. For each infection, we compute the basic reproductive numbers $\mathbb{R}_{01} <1$, and $\mathbb{R}_{02}<1$. To determine the realistic values of the model parameters, data regarding COVID-19 instances was obtained from China National Health Commission.Sensitivity study employing the PRCC technique to look into the key variables that affect $\mathbb{R}_{01}$, or $\mathbb{R}_{02}<1$ decrease or increase. We show the numerical simulation of the model using non-standard finite difference scheme (NSFD) and stochastic numerical method. On the basis of these mentioned numerical methods, some graphical results for the model with sensitive parameters are provided.