Abstract
In this paper, we develop a deterministic and stochastic mathematical model to study the effect of contaminated foods on human health by spreading media awareness. A predator–prey SI model with media-induced response function is considered. In the deterministic case, the model has three equilibria: trivial, disease-free, and endemic. While the endemic equilibria exist for low media impact provided R0>1. Here, the trivial equilibrium is always unstable. However, the disease-free equilibrium exhibits local and global asymptotically stable behavior provided that R0<1. The conditions for the local behavior of endemic equilibrium are also determined along with the existence of Hopf bifurcation. Further, the impact of external interference is studied for the stochastic model. The stochastic model has a unique global positive solution which is ultimately bounded. The stochastic model also demonstrates asymptotic behavior around disease-free and endemic equilibria. Additionally, optimal control theory has been employed to explore deterministic and stochastic optimal control systems in depth. Finally, the analytical results are validated using some numerical simulations.
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