Discrete-Time Eco-epidemiological Model with Disease in Prey and Holling Type III Functional Response

2016 ◽  
pp. 329-341
Author(s):  
Elizabeth Sebastian ◽  
Priyanka Victor ◽  
Preethi Victor
Keyword(s):  
Functional Response ◽  
Discrete Time ◽  
Epidemiological Model ◽  
Type Iii ◽  
Disease In Prey

scholarly journals Fluctuations in population densities inform stability mechanisms in host-parasitoid interactions

2021 ◽  
Author(s):  
Abhyudai Singh
Keyword(s):  
Population Dynamics ◽  
Population Density ◽  
Functional Response ◽  
Discrete Time ◽  
Host Population ◽  
Reproduction Rate ◽  
Population Densities ◽  
Type Iii ◽  
Time Formalism ◽  
Large Fluctuations

AbstractPopulation dynamics of host-parasitoid interactions has been traditionally studied using a discrete-time formalism starting from the classical work of Nicholson and Bailey. It is well known that differences in parasitism risk among individual hosts can stabilize the otherwise unstable equilibrium of the Nicholson-Bailey model. Here, we consider a stochastic formulation of these discrete-time models, where the host reproduction is a random variable that varies from year to year and drives fluctuations in population densities. Interestingly, our analysis reveals that there exists an optimal level of heterogeneity in parasitism risk that minimizes the extent of fluctuations in the host population density. Intuitively, low variation in parasitism risk drives large fluctuations in the host population density as the system is on the edge of stability. In contrast, high variation in parasitism risk makes the host equilibrium sensitive to the host reproduction rate, also leading to large fluctuations in the population density. Further results show that the correlation between the adult host and parasitoid densities is high for the same year, and gradually decays to zero as one considers cross-species correlations across different years. We next consider an alternative mechanism of stabilizing host-parasitoid population dynamics based on a Type III functional response, where the parasitoid attack rate accelerates with increasing host density. Intriguingly, this nonlinear functional response makes qualitatively different correlation signatures than those seen with heterogeneity in parasitism risk. In particular, a Type III functional response leads to uncorrelated adult and parasitoid densities in the same year, but high cross-species correlation across successive years. In summary, these results argue that the cross-correlation function between population densities contains signatures for uncovering mechanisms that stabilize consumer-resource population dynamics.

scholarly journals The The Dynamics of a Prey-Predator Model with Infectious Disease in Prey: Role of Media Coverage

2021 ◽  
pp. 4930-4952
Author(s):  
Wassan Hussein ◽  
Huda Abdul Satar
Keyword(s):  
Infectious Disease ◽  
Global Stability ◽  
Numerical Simulations ◽  
Functional Response ◽  
Media Coverage ◽  
Epidemiological Model ◽  
Local Bifurcation ◽  
Predator Model ◽  
Disease In Prey

In this paper, an eco-epidemiological model with media coverage effect is proposed and studied. A prey-predator model with modified Leslie-Gower and functional response is studied. An  -type of disease in prey is considered.  The existence, uniqueness and boundedness of the solution of the model are discussed. The local and global stability of this system are carried out. The conditions for the persistence of all species are established. The local bifurcation in the model is studied. Finally, numerical simulations are conducted to illustrate the analytical results.

Stability and permanence of a discrete-time two-prey one-predator system with Holling Type-III functional response

2018 ◽  
Vol 117 ◽  
pp. 240-248 ◽  
Author(s):  
Ritwick Banerjee ◽  
Pritha Das ◽  
Debasis Mukherjee
Keyword(s):  
Functional Response ◽  
Discrete Time ◽  
Type Iii ◽  
Predator System

scholarly journals Stochasticity in host-parasitoid models informs mechanisms regulating population dynamics

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Abhyudai Singh
Keyword(s):  
Population Dynamics ◽  
Population Density ◽  
Functional Response ◽  
Discrete Time ◽  
Host Population ◽  
Reproduction Rate ◽  
Population Densities ◽  
Type Iii ◽  
Time Formalism ◽  
Large Fluctuations

AbstractPopulation dynamics of host-parasitoid interactions have been traditionally studied using a discrete-time formalism starting from the classical work of Nicholson and Bailey. It is well known that differences in parasitism risk among individual hosts can stabilize the otherwise unstable equilibrium of the Nicholson-Bailey model. Here, we consider a stochastic formulation of these discrete-time models, where the host reproduction is a random variable that varies from year to year and drives fluctuations in population densities. Interestingly, our analysis reveals that there exists an optimal level of heterogeneity in parasitism risk that minimizes the extent of fluctuations in the host population density. Intuitively, low variation in parasitism risk drives large fluctuations in the host population density as the system is on the edge of stability. In contrast, high variation in parasitism risk makes the host equilibrium sensitive to the host reproduction rate, also leading to large fluctuations in the population density. Further results show that the correlation between the adult host and parasitoid densities is high for the same year, and gradually decays to zero as one considers cross-species correlations across different years. We next consider an alternative mechanism of stabilizing host-parasitoid population dynamics based on a Type III functional response, where the parasitoid attack rate accelerates with increasing host density. Intriguingly, this nonlinear functional response makes qualitatively different correlation signatures than those seen with heterogeneity in parasitism risk. In particular, a Type III functional response leads to uncorrelated adult and parasitoid densities in the same year, but high cross-species correlation across successive years. In summary, these results argue that the cross-correlation function between population densities contains signatures for uncovering mechanisms that stabilize consumer-resource population dynamics.

BIFURCATION AND CHAOS IN A DISCRETE PREDATOR–PREY MODEL WITH HOLLING TYPE-III FUNCTIONAL RESPONSE AND HARVESTING EFFECT

2021 ◽  
pp. 1-28
Author(s):  
ANURAJ SINGH ◽  
PREETI DEOLIA
Keyword(s):  
Functional Response ◽  
Sufficient Conditions ◽  
Flip Bifurcation ◽  
Bifurcation Structure ◽  
Bifurcation And Chaos ◽  
Predator Prey ◽  
Type Iii ◽  
Predator Prey Model ◽  
Prey Model ◽  
Wide Range

In this paper, we study a discrete-time predator–prey model with Holling type-III functional response and harvesting in both species. A detailed bifurcation analysis, depending on some parameter, reveals a rich bifurcation structure, including transcritical bifurcation, flip bifurcation and Neimark–Sacker bifurcation. However, some sufficient conditions to guarantee the global asymptotic stability of the trivial fixed point and unique positive fixed points are also given. The existence of chaos in the sense of Li–Yorke has been established for the discrete system. The extensive numerical simulations are given to support the analytical findings. The system exhibits flip bifurcation and Neimark–Sacker bifurcation followed by wide range of dense chaos. Further, the chaos occurred in the system can be controlled by choosing suitable value of prey harvesting.

scholarly journals Analysis of an Ecoepidemiological Model with Prey Refuges

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Shufan Wang ◽  
Zhihui Ma
Keyword(s):  
Functional Response ◽  
Contact Process ◽  
Global Perspective ◽  
Basic System ◽  
Stability Behavior ◽  
The Stability ◽  
Holling Iii Functional Response ◽  
Disease In Prey ◽  
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.

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.

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