scholarly journals The stability of a perturbed eco-epidemiological model with Holling type II functional response by white noise

2015 ◽  
Vol 20 (1) ◽  
pp. 295-321
Author(s):  
Qiumei Zhang ◽  
◽  
Daqing Jiang ◽  
Li Zu
Keyword(s):  
White Noise ◽  
Functional Response ◽  
Epidemiological Model ◽  
Type Ii ◽  
The Stability ◽  
Type Ii Functional Response

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.

STABILITY AND HOPF BIFURCATION OF A PREDATOR–PREY SYSTEM WITH TIME DELAY AND HOLLING TYPE-II FUNCTIONAL RESPONSE

2009 ◽  
Vol 02 (02) ◽  
pp. 139-149 ◽  
Author(s):  
LINGSHU WANG ◽  
RUI XU ◽  
GUANGHUI FENG
Keyword(s):  
Time Delay ◽  
Functional Response ◽  
Type Ii ◽  
Normal Form Theory ◽  
Predator Prey ◽  
Center Manifold Theorem ◽  
Predator Prey Model ◽  
Form Theory ◽  
The Stability ◽  
Type Ii Functional Response

A predator–prey model with time delay and Holling type-II functional response is investigated. By choosing time delay as the bifurcation parameter and analyzing the associated characteristic equation of the linearized system, the local stability of the system is investigated and Hopf bifurcations are established. The formulae determining the direction of bifurcations and the stability of bifurcating periodic solutions are given by using the normal form theory and center manifold theorem. Numerical simulations are carried out to illustrate the theoretical results.

scholarly journals Long-Time Behaviours of a Stochastic Predator-Prey System with Holling-Type II Functional Response and Regime Switching

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Weili Kong ◽  
Yuanfu Shao
Keyword(s):  
White Noise ◽  
Functional Response ◽  
Regime Switching ◽  
Type Ii ◽  
Stochastic Permanence ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Long Time ◽  
Type Ii Functional Response

Considering the impacts of white noise, Holling-type II functional response, and regime switching, we formulate a stochastic predator-prey model in this paper. By constructing some suitable functionals, we establish the sufficient criteria of the stationary distribution and stochastic permanence. By numerical simulations, we illustrate the results and analyze the influence of regime switching on the dynamics.

scholarly journals Hopf Bifurcation and Hybrid Control of a Delayed Ecoepidemiological Model with Nonlinear Incidence Rate and Holling Type II Functional Response

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Miao Peng ◽  
Zhengdi Zhang ◽  
C. W. Lim ◽  
Xuedi Wang
Keyword(s):  
Hopf Bifurcation ◽  
Incidence Rate ◽  
Functional Response ◽  
Hybrid Control ◽  
Type Ii ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Center Manifold Theorem ◽  
The Stability ◽  
Type Ii Functional Response

Hopf bifurcation analysis of a delayed ecoepidemiological model with nonlinear incidence rate and Holling type II functional response is investigated. By analyzing the corresponding characteristic equations, the conditions for the stability and existence of Hopf bifurcation for the system are obtained. In addition, a hybrid control strategy is proposed to postpone the onset of an inherent bifurcation of the system. By utilizing normal form method and center manifold theorem, the explicit formulas that determine the direction of Hopf bifurcation and the stability of bifurcating period solutions of the controlled system are derived. Finally, some numerical simulation examples confirm that the hybrid controller is efficient in controlling Hopf bifurcation.

scholarly journals Demography and feeding behavior of Stenostomum leucops (Dugés, 1828)

2016 ◽  
Vol 75 (s1) ◽  
Author(s):  
Alma R. Núñez-Ortiz ◽  
Sarma Nandini ◽  
S.S.S. Nandini
Keyword(s):  
Functional Response ◽  
Food Preference ◽  
Type Ii ◽  
Final Density ◽  
Two Temperatures ◽  
The Difference ◽  
Growth Experiments ◽  
Pelagic Communities ◽  
Type Ii Functional Response ◽  
Planktonic Communities

<p>Freshwater turbellarians, despite their mainly benthic habits, interact with pelagic communities of rotifers and cladocerans. However, very little is known about their demographic characteristics, food preference and functional response. To fill that gap we studied one of the most widely spread species, <em>Stenostomum leucops</em>.  We conducted population growth experiments using abundant food (several rotifer and cladocerans species). To evaluate possible impact of <em>S. leucops</em> on planktonic communities, we conducted prey preference experiments at two temperatures: 18 and 23°C. The number of rotifers and cladocerans consumed was calculated by the difference between the initial and final density. We found that diets supplemented with fresh algae achieved higher <em>S. leucops</em> densities than those with detritus supplements in their diets. In the case of animal diets, <em>Euchlanis dilatata</em> allowed <em>S. leucops</em> reach higher densities than the other zooplankton species; <em>E. dilatata</em> was positively selected for in the selectivity study at both 18 and 23°C.  <em>Stenostomum leucops</em> showed a type II functional response on rotifers and the cladoceran <em>Alona glabra</em>. Our results suggest that <em>S. leucops</em> select their prey according to their vulnerability using different mechanisms, which optimize their food intake.</p>

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