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.

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 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>

scholarly journals PREFERENSI DAN TANGGAP FUNGSIONAL PARASITOID HEMIPTARSENUS VARICORNIS (GIRAULT) (HYMENOPTERA: EULOPHIDAE) PADA LARVA LALAT PENGOROK DAUN KENTANG

2009 ◽  
Vol 9 (1) ◽  
pp. 15-21
Author(s):  
Hidrayani Hidrayani ◽  
Aunu Rauf ◽  
S. Sosromarsono ◽  
U. Kartosuwondo
Keyword(s):  
Regression Analysis ◽  
Functional Response ◽  
Preference Test ◽  
Handling Time ◽  
Equation Model ◽  
Type Ii ◽  
Female Parasitoid ◽  
Host Abundance ◽  
Liriomyza Huidobrensis ◽  
Type Ii Functional Response

The preference and functional response of Parasitoid Hemiptarsenus varicornis (Girault) (Hymenoptera:Eulophidae) on host larvae of potato leafminers. The preference of Hemiptarsenus varicornis (Girault) on host larvae of potato leafminers (Liriomyza huidobrensis) and their  functional response on host abundance were studied in laboratory. The preference test was conducted by releasing a female parasitoid in a cage containing two redbean leaves, one with 2nd instar and another one with 3rd instar.  The functional response test was conducted by providing 3rd instar  with density 1, 4, 6, 8, 10, and 13  larvae  per leaf. The result showed that  H. varicornis had the preference on 3rd instar  larvae compared to 2nd instar, either for parasitisation or paralysis. Based on logistic regression analysis it was found that the parasitoid showed type II functional response on the increase of host abundance. The searching rate (a) and handling time (Th) for paralysis were 0.038 and 1.473 based on disk equation model, and 0.076 and 2.060 on ramdom equation model.  For parasitisation activity, the value of  a and Th were  0.012 and 4.649 based on disk equation model, and 0.014 and 5.075 on random equation model.

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