scholarly journals An eco-epidemiological model with general functional response of predator to prey

2021 ◽  
Author(s):  
Lopo de Jesus ◽  
César Silva ◽  
Helder Vilarinho
Keyword(s):  
Functional Response ◽  
Iterative Process ◽  
Epidemiological Model ◽  
Epidemiological Models ◽  
Free System ◽  
Disease Free ◽  
Infected Prey

We consider a nonautonomous eco-epidemiological model with general functions for predation on infected and uninfected preys as well as general functions associated to the vital dynamics of the susceptible prey and predator populations. We obtain persistence and extinction results for the infected prey based on assumptions on auxiliary systems constructed from the disease-free system. We moreover consider an iterative process that can improve the extinction results. We apply our results to general eco-epidemiological models that include several examples existent in the literature.

scholarly journals Stability analysis of an ecoepidemiological model consisting of a prey and tow competing predators with Si-disease in prey and toxicant

2020 ◽  
Vol 99 (3) ◽  
pp. 55-61
Author(s):  
Evren Hincal ◽  
◽  
Shorsh Mohammed ◽  
Bilgen Kaymakamzade ◽  
◽  
...  
Keyword(s):  
Stability Analysis ◽  
Functional Response ◽  
Linear Functional ◽  
Prey Species ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Epidemiological Models ◽  
Proposed Model ◽  
Infected Prey ◽  
Disease In Prey

In the present paper, we study two eco-epidemiological models. The first one consists of a prey and two competing predators with SI-disease in prey species spreading by contacts between susceptible prey and infected prey. This model assumes linear functional response. The second model is the modification of the first one when the effect of toxicant is taken into account. In this paper, we examine the dynamical behavior of non-survival and free equilibrium points of our proposed model.

PROPER PREDATION MAKES THE SYSTEM DISEASE FREE — CONCLUSION DRAWN FROM AN ECO-EPIDEMIOLOGICAL MODEL

2006 ◽  
Vol 14 (04) ◽  
pp. 599-616 ◽  
Author(s):  
SAMRAT CHATTERJEE ◽  
M. BANDYOPADHYAY ◽  
J. CHATTOPADHYAY
Keyword(s):  
Chaotic Dynamics ◽  
Chaotic Behavior ◽  
Epidemiological Model ◽  
Global Dynamics ◽  
System Parameters ◽  
System Disease ◽  
Simulation Results ◽  
Disease Free ◽  
Infected Prey ◽  
Predation Rates

In the present paper, an eco-epidemiological model consisting of susceptible prey, infected prey and predator has been proposed and analyzed. We have obtained conditions for the existence and persistence of all the three populations. To study the global dynamics of the system, numerical simulations have been performed. Our simulation results show that the system enters into quasi-periodic solutions or chaotic depending upon the choice of system parameters. To confirm the chaotic behavior of the system, we have calculated Lyapunov exponent and constructed Poincare section. Our analysis reveals that the infection and predation rates specially on the infected prey population are the key parameters that play crucial roles for controlling the chaotic dynamics of the system.

A strategy for a disease-free system- an eco-epidemiological model based study

2016 ◽  
Vol 55 (1-2) ◽  
pp. 563-590 ◽  
Author(s):  
Krishna Pada Das ◽  
Sudip Samanta ◽  
Santosh Biswas ◽  
Ali Saleh Alshomrani ◽  
Joydev Chattopadhyay
Keyword(s):  
Epidemiological Model ◽  
Free System ◽  
Model Based ◽  
Disease Free

Predator-dependent transmissible disease spreading in prey under Holling type-II functional response

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Dipankar Ghosh ◽  
Prasun K. Santra ◽  
Abdelalim A. Elsadany ◽  
Ghanshaym S. Mahapatra
Keyword(s):  
Functional Response ◽  
Prey Species ◽  
Linearization Method ◽  
Logistic Growth ◽  
Type Ii ◽  
Disease Spreading ◽  
Predator Interactions ◽  
The Stability ◽  
Infected Prey ◽  
Type Ii Functional Response

Abstract This paper focusses on developing two species, where only prey species suffers by a contagious disease. We consider the logistic growth rate of the prey population. The interaction between susceptible prey and infected prey with predator is presumed to be ruled by Holling type II and I functional response, respectively. A healthy prey is infected when it comes in direct contact with infected prey, and we also assume that predator-dependent disease spreads within the system. This research reveals that the transmission of this predator-dependent disease can have critical repercussions for the shaping of prey–predator interactions. The solution of the model is examined in relation to survival, uniqueness and boundedness. The positivity, feasibility and the stability conditions of the fixed points of the system are analysed by applying the linearization method and the Jacobian matrix method.

Periodic Solutions of a Delayed Eco-Epidemiological Model with Infection-Age Structure and Holling Type II Functional Response

2020 ◽  
Vol 30 (01) ◽  
pp. 2050011 ◽  
Author(s):  
Peng Yang ◽  
Yuanshi Wang
Keyword(s):  
Hopf Bifurcation ◽  
Functional Response ◽  
Age Structure ◽  
Epidemiological Model ◽  
Type Ii ◽  
Epidemic Disease ◽  
Semilinear Equations ◽  
Infection Age ◽  
Coexistence Equilibrium ◽  
Type Ii Functional Response

This paper is devoted to the study of a new delayed eco-epidemiological model with infection-age structure and Holling type II functional response. Firstly, the disease transmission rate function among the predator population is treated as the piecewise function concerning the incubation period [Formula: see text] of the epidemic disease and the model is rewritten as an abstract nondensely defined Cauchy problem. Besides, the prerequisite which guarantees the presence of the coexistence equilibrium is achieved. Secondly, via utilizing the theory of integrated semigroup and the Hopf bifurcation theorem for semilinear equations with nondense domain, it is found that the model exhibits a Hopf bifurcation near the coexistence equilibrium, which suggests that this model has a nontrivial periodic solution that bifurcates from the coexistence equilibrium as the bifurcation parameter [Formula: see text] crosses the bifurcation critical value [Formula: see text]. That is, there is a continuous periodic oscillation phenomenon. Finally, some numerical simulations are shown to support and extend the analytical results and visualize the interesting phenomenon.

Mathematical Study of a Class of Epidemiological Models with Multiple Infectious Stages

2020 ◽  
Vol 21 (3-4) ◽  
pp. 259-274
Author(s):  
S. Bowong ◽  
A. Temgoua ◽  
Y. Malong ◽  
J. Mbang
Keyword(s):  
Theoretical Study ◽  
Reproduction Number ◽  
Communicable Disease ◽  
Transmission Dynamics ◽  
Asymptotically Stable ◽  
Epidemiological Models ◽  
Mathematical Study ◽  
Globally Asymptotically Stable ◽  
Disease Free

AbstractThis paper deals with the mathematical analysis of a general class of epidemiological models with multiple infectious stages for the transmission dynamics of a communicable disease. We provide a theoretical study of the model. We derive the basic reproduction number $\mathcal R_0$ that determines the extinction and the persistence of the infection. We show that the disease-free equilibrium is globally asymptotically stable whenever $\mathcal R_0 \leq 1$, while when $\mathcal R_0 \gt 1$, the disease-free equilibrium is unstable and there exists a unique endemic equilibrium point which is globally asymptotically stable. A case study for tuberculosis (TB) is considered to numerically support the analytical results.

scholarly journals An SIRS epidemic model of Japanese Encephalitis

1994 ◽  
Vol 17 (2) ◽  
pp. 347-355 ◽  
Author(s):  
B. B. Mukhopadhyay ◽  
P. K. Tapaswi
Keyword(s):  
Japanese Encephalitis ◽  
Epidemic Model ◽  
Human Population ◽  
Control Measure ◽  
Passive Immunization ◽  
Coupled System ◽  
Reproductive Rate ◽  
Free System ◽  
Sirs Epidemic Model ◽  
Disease Free

An epidemiological model of the dynamics of Japanese Encephalitis (J.E.) spread coupling the SIRS (Susceptible/Infected/Removal/Susceptible) models of J.E. spread in the reservoir population and in the human population has been proposed. The basic reproductive rateR(0)in the coupled system has been worked out. Using Aron's results (cf. [1] and [2]), it has been observed that the disease-free system is stable in this coupled system also, ifR(0)is less than unity, and ifR(0)is greater than unity, the disease-free system is unstable and there exists a unique stable endemic equilibrium.The model also shows that in contrast to Aron's observations, loss of immunity is independent of the rate of exposure to the disease. This observation sheds light on the control measure of J.E. by vaccination. Passive immunization, i.e., administration of antibody at recurrent intervals is the correct method of vaccination to eradicate the disease.

OCCURRENCE OF CHAOS AND ITS POSSIBLE CONTROL IN A PREDATOR-PREY MODEL WITH DENSITY DEPENDENT DISEASE-INDUCED MORTALITY ON PREDATOR POPULATION

2010 ◽  
Vol 18 (02) ◽  
pp. 399-435 ◽  
Author(s):  
KRISHNA PADA DAS ◽  
SAMRAT CHATTERJEE ◽  
J. CHATTOPADHYAY
Keyword(s):  
Equilibrium Points ◽  
Dynamical Behaviour ◽  
Predator Population ◽  
Epidemiological Models ◽  
Predator Prey ◽  
Density Dependent ◽  
Predator Prey Model ◽  
Chaotic Nature ◽  
Mortality Function ◽  
Infected Prey

Eco-epidemiological models are now receiving much attention to the researchers. In the present article we re-visit the model of Holling-Tanner which is recently modified by Haque and Venturino1 with the introduction of disease in prey population. Density dependent disease-induced predator mortality function is an important consideration of such systems. We extend the model of Haque and Venturino1 with density dependent disease-induced predator mortality function. The existence and local stability of the equilibrium points and the conditions for the permanence and impermanence of the system are worked out. The system shows different dynamical behaviour including chaos for different values of the rate of infection. The model considered by Haque and Venturino1 also exhibits chaotic nature but they did not shed any light in this direction. Our analysis reveals that by controlling disease-induced mortality of predator due to ingested infected prey may prevent the occurrence of chaos.

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