Computational analysis of the coronavirus epidemic model involving nonlinear stochastic differential equations

Abstract

Stochastic methods significantly solve stochastic differential equations such as stochastic equations with a delay, stochastic fractional and fractal equations, stochastic partial differential equations, and many more. The coronavirus is still a threat to humans and puts people in danger. The model is a symmetric and compatible distribution family. In this case, the present model contains seven sub-populations of humans: susceptible, exposed, infected, quarantined, vaccinated, recovered, and dead. Two deterministic to stochastic formation types are studied, namely, transition probabilities and nonparametric perturbations. The positivity and boundedness of the stochastic model are analyzed. The stochastic Euler, stochastic Runge–Kutta, and Euler–Maruyama methods solve the stochastic system. Unfortunately, many issues originate, such as negativity, boundedness, and violation of dynamical consistency. The nonstandard finite difference method is designed in the sense of stochasticity to restore the dynamic properties of the model. In the end, simulations are carried out in contrast to deterministic and stochastic solutions. Overall, our findings shed light on the underlying mechanisms of COVID-19 dynamics and the influence of environmental factors on the spread of the disease, which can help make informed policy decisions and public health interventions.