Role of horizontal incidence in the occurrence and control of chaos in an eco-epidemiological system

Abstract

A predator-prey model with disease in the prey population is proposed and analysed. The mode of disease transmission plays an important role in such dynamics. Keeping this factor in mind, we observe the dynamics of such a system for simple mass action incidence and standard incidence. Our observations indicate that the phenomenon of rarity or non-occurrence of chaos in our proposed model is well defined if the mode of disease transmission follows standard incidence. Moreover, using the method of Latin hypercube sampling, we show that the region of stability increases if the disease transmission follows the standard incidence law.

Bifurcation and Dynamic Analyses of a Diseased Predator-prey Model With Prey Refuge

“…The figure (8) shows the dynamical changes of the system (2) at the rate of refuge m = 0.3. We can observe in that figure (5) the density of the population of susceptible prey decreases as the refuge constant increases; we also observe an increase in the population of infected prey as the refuge constant increases from 0.2 to 0.7.…”

“…The basic SIS model was proposed and investigated by more research revealing that eco-epidemiological models, which mix the two categories above, are effective [2]. Thereafter, some researchers proposed and investigated the different predatorprey models that included infection in the prey population [3][4][5][6]. Moreover, there are numerous studies on prey-predator models with diseased predator populations [3,[7][8][9].…”

Complex dynamics and its stabilization in an eco-epidemiological model with alternative food

“…They have tried to explain the unusual deaths of fish and fish eating birds in the Salton Sea using the simulation results and they have also suggested some possible measures to avoid chaos in such natural systems. Chatterjee et al (2007) considered the model proposed by Chatterjee et al (2006) and modified the model by assuming that the disease transmission follows standard incidence law. They compared the dynamical nature of the two systems numerically for a wider range of force of infection.…”

Chaos in disease outbreaks among prey

“…Most epidemics are notoriously unpredictable 16 , particularly in the cases of zoonoses and vector-borne diseases 17 , and it has previously been considered whether seasonality or noise might drive chaos in the dynamics of certain childhood diseases 16,18,19 . Furthermore, a few papers have examined the potential chaotic behaviour of enzootics in predator-prey ecosystems, usually with infection in the predator 20,21 , but also in the prey 22 . However, to our knowledge, chaos and disease have not been studied in the context of generalist predators, which must be assumed to be more common in nature than entirely specialist predators.…”