Non-standard Computational Analysis of the Stochastic COVID-19 Pandemic Model: An Application of Computational Biology

Aslam Noor, Muhammad; Raza, Ali; Shoaib Arif, Muhammad; Rafiq, Muhammad; Sooppy Nisar, Kottakkaran; Khan, Ilyas; Abdelwahab, Sayed F.

The present study is conducted to analyse the computational dynamical analysis of the stochastic susceptible-infected-recovered pandemic model of the novel coronavirus. We adopted two ways for stochastic modelling like as transition probabilities and parametric perturbation techniques. We applied different and well-known computational methods like Euler Maruyama, stochastic Euler, and stochastic Runge Kutta to study the dynamics of the model mentioned above. Unfortunately, these computational methods do not restore the dynamical properties of the model like positivity, boundedness, consistency, and stability in the sense of biological reasoning, as desired. Then, for the given stochastic model, we developed a stochastic non-standard finite difference method. Following that, several theorems are presented to support the proposed method, which is shown to satisfy all of the model's dynamical properties. To that end, several simulations are presented to compare the proposed method's efficiency to that of existing stochastic methods.