Optimal control theory of a novel stochastic human norovirus model and vaccine development

Abstract

Norovirus is a contagious disease that causes diarrhea and vomiting and has a significant impact on humanity in terms of medical costs, deaths and mortalities. In this research work, the stochastic modeling techniques are utilized and a novel human norovirus model is investigated keeping in view the contamination of food and water with vaccination effects. It is proved that the model has a unique global solution and by using Lyapunov function theory, sufficient conditions are derived under which the proposed model has a unique ergodic stationary distribution for [Formula: see text]. It is observed that the disease will extinct out of the population whenever [Formula: see text]. To demonstrate the analytical results, two independent examples are depicted graphically by using standard numerical algorithm. To reduce the spread of the virus, we employed certain control measures and an optimal control problem is presented. To further validate the obtained analytical results, additional graphical solutions were generated. This study might provide a robust theoretical framework for a global understanding of chronic communicable illnesses. Our method also aims to provide a method for producing Lyapunov functions, which can be used to explore the stationary distribution of disease models having nonlinear stochastic perturbations.