Dynamics of a stage-structured SI model for food adulteration with media-induced response function

Abstract

In this work, an eco-epidemic predator–prey model with media-induced response function for the interaction of humans with adulterated food is developed and studied. The human population is divided into two main compartments, namely, susceptible and infected. This system has three equilibria; trivial, disease-free and endemic. The trivial equilibrium is forever an unstable saddle position, while the disease-free state is locally asymptotically stable under a threshold of delay parameter tau as well as {mathcal {R}}_0<1. The sufficient conditions for the local stability of the endemic equilibrium point are further explored when min {{mathcal {R}}_0,{mathcal {R}}_0^*}>1 . The conditions for the occurrence of the stability switching are also determined by taking infection delay time as a critical parameter, which concludes that the delay can produce instability and small amplitude oscillations of population masses via Hopf bifurcations. Further, we study the stability and direction of the Hopf bifurcations using the center manifold argument. Furthermore, some numerical simulations are conducted to validate our analytical findings and discuss their biological inferences. Finally, the normalized forward sensitivity index is used to perform the sensitivity analysis of {mathcal {R}}_0 and {mathcal {R}}_0^*.