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 as well as . The sufficient conditions for the local stability of the endemic equilibrium point are further explored when . 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 and .

Eco-epidemic Dynamics with Infected Communicable Infection from Prey to Predator: Effect of Recovery Delay for Predator

“…Moreover, Khalaf et al [31] have presented a hypothesis wherein predators become infected by consuming prey that is already infected. Additionally, several researchers [32][33][34] have incorporated the concept of infection delay into their mathematical models within the field of population dynamics. These investigations seek to elucidate the efficacy of infection delay at the dynamics of prey-predator interactions within populations.…”

A brief discussion about a predator-prey model including disease in predators with the delay effect

“…The predator-prey model has been used broadly throughout the past few decades since the pioneering work of Lotka [27] and Volterra [52], and will continue to be utilized to comprehend the dynamics of interacting populations. The Lotka-Volterra model has experienced extensive modifications through various aspects [33,53,50,18,7], such as improving the predator's functional response to enhance the realistic application of the suggested prey-predator models [40,19,20,34]. The functional response, which is determined as the amount of prey caught per predator per unit time, depends on many factors like the prey density, the converting efficiency, the attacking efficiency, the handling, and gestating time.…”