Bifurcation analysis of an age‐structured prey–predator model with infection developed in prey

Abstract

In this work, we propose an age‐structured prey–predator model with infection developed in the prey population. Our main goal is to distinguish the effect of the predator maturation measured by the age on the interaction between the predator and the prey, even on the spread of the infectious disease. However, it is obtained that the minimal maturation duration can affect the behavior of the solution, where it can lead to the existence of periodic solutions generated by the presence of Hopf bifurcation for three different equilibrium states. The obtained mathematical results are checked numerically using graphical illustrations.

Dynamics analysis of a predator–prey fractional-order model incorporating predator cannibalism and refuge

“…Predator-prey interaction, as the basis of the food chain, is among the most essential ecological issues. In numerous published research, mathematical models have been developed to explain the dynamics of Predator-prey interaction, such as by incorporating social behavior [1,2], age structure [3,4], ratio-dependent functional response [5,6], harvesting [7,8], and so on. The Predator-prey model is still being developed by considering many factors that occur in nature.…”

A predator–prey system with prey social behavior and generalized Holling III functional response: Role of predator‐taxis on spatial patterns

“…The pioneering works of Lotka [1] and Volterra [2] on predator-prey systems have generated a wealth of research on biological models that involve multiple species [3][4][5], with wide-ranging applications in ecology and biology. In mathematical ecology, one of the fundamental goals is to understand the dynamic relationship between species and their impacts on the ecosystems [6].…”

Spatially inhomogeneous bifurcating periodic solutions induced by nonlocal competition in a predator–prey system with additional food

“…Predator–prey relationship is a common population interaction relationship in nature; many scholars have studied this kind of models 1–4 . Bentout et al 5 mainly discussed the effect of predation on disease transmission in predator–prey populations, where the prey has social behavior.…”

“…Predator-prey relationship is a common population interaction relationship in nature; many scholars have studied this kind of models. [1][2][3][4] Bentout et al 5 mainly discussed the effect of predation on disease transmission in predator-prey populations, where the prey has social behavior. Djilali et al 6 proposed a delayed predator-prey model in the presence of prey herd behavior and obtained that the model can undergo Hopf bifurcation in both the absence and presence of time lags and forward bifurcation in the absence of time delay.…”