Dynamics of nonautonomous eco-pidemiological models

We consider a general eco-epidemiological model which includes a large variety of eco-epidemiological models available in the literature. We assume that the parameters are time dependent and we consider general functions for the predation on infected and uninfected prey and also for the vital dynamics of uninfected prey and predator populations. We studied this model in four scenarios: non-autonomous, periodic, discrete and random. In the non-autonomous and discrete case we discussed the uniform strong persistence and extinction of the disease, in the periodic case, we studied the existence of an endemic periodic orbit, and nally, in the random case we studied the existence of random global attractors.Nesta tese consideramos um modelo eco-epidemiológico geral que inclui uma grande variedade de modelos eco-epidemiológicos presentes na literatura. Assumimos que os parâmetros dependem do tempo e consideramos funções gerais para a predação de presas infectadas e não infectadas e também para a dinâmica vital de presas não infectadas e da população de predadores. Estudamos estes modelos em quatro cenários: não-autónomo geral, periódico, discreto e aleatório. Nos casos não-autónomo geral e discreto analisamos a persistência forte e extinção da doença, no caso periódico estudamos as condições para a existência de uma órbita periódica endémica e, finalmente, no caso aleatório estudamos a existência de atratores globais aleatórios

Analysis of an Eco-Epidemiological Model under Optimal Control Measures for Infected Prey

This paper examines the analysis of an eco-epidemiological model with optimal control strategies for infected prey. A model is proposed and analyzed qualitatively using the stability theory of the differential equations. A local and global study of the model is performed around the disease-free equilibrium and the endemic equilibrium to analyze the global stability using the Lyapunov function. The time-dependent control is introduced into the system to determine the best strategy for controlling the disease. The results obtained suggested the separation of the infected population plays a vital role in disease elimination

Dynamics of prey–predator model with strong and weak Allee effect in the prey with gestation delay

This study proposes two prey–predator models with strong and weak Allee effects in prey population with Crowley–Martin functional response. Further, gestation delay of the predator population is introduced in both the models. We discussed the boundedness, local stability and Hopf-bifurcation of both nondelayed and delayed systems. The stability and direction of Hopfbifurcation is also analyzed by using Normal form theory and Center manifold theory. It is shown that species in the model with strong Allee effect become extinct beyond a threshold value of Allee parameter at low density of prey population, whereas species never become extinct in weak Allee effect if they are initially present. It is also shown that gestation delay is unable to avoiding the status of extinction. Lastly, numerical simulation is conducted to verify the theoretical findings.&nbsp

Stability analysis of an eco-epidemiological model incorporating a prey refuge

The present paper deals with the problem of a predator-prey model incorporating a prey refuge with disease in the prey-population. We assume the predator population will prefer only infected population for their diet as those are more vulnerable. Dynamical behaviours such as boundedness, permanence, local and global stabilities are addressed. We have also studied the effect of discrete time delay on the model. The length of delay preserving the stability is also estimated. Computer simulations are carried out to illustrate our analytical findings

Dynamical Properties of a Delay Prey-Predator Model with Disease in the Prey Species Only

A three-dimensional ecoepidemiological model with delay is considered. We first investigate the existence and stability of the equilibria. We then study the effect of the time delay on the stability of the positive equilibrium. The existence of a Hopf bifurcation at the positive equilibrium is obtained through the study of an exponential polynomial equation with delay-dependent coefficients. Numerical simulation with a hypothetical set of data has been carried out to support the analytical findings

Analysis of an Ecoepidemiological Model with Prey Refuges

An ecoepidemiological system with prey refuges and disease in prey is proposed. Bilinear incidence and Holling III functional response are used to model the contact process and the predation process, respectively. We will study the stability behavior of the basic system from a local to a global perspective. Permanence of the considered system is also investigated