Mathematical Analysis of an Eco-Epidemic Model with Different Functional Responses of Healthy and Infected Predators on Prey Species

2020 ◽  
Vol 9 (4) ◽  
pp. 667-684
Author(s):  
Harekrishna Das ◽  
Absos Ali Shaikh ◽  
Sahabuddin Sarwardi
Keyword(s):  
Mathematical Analysis ◽  
Epidemic Model ◽  
Prey Species ◽  
Functional Responses

scholarly journals Permanence of Periodic Predator-Prey System with Functional Responses and Stage Structure for Prey

2008 ◽  
Vol 2008 ◽  
pp. 1-15 ◽  
Author(s):  
Can-Yun Huang ◽  
Min Zhao ◽  
Hai-Feng Huo
Keyword(s):  
Functional Response ◽  
Prey Species ◽  
Necessary Conditions ◽  
Stage Structure ◽  
Functional Responses ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Sufficient And Necessary Conditions ◽  
Holling Ii Functional Response

A stage-structured three-species predator-prey model with Beddington-DeAngelis and Holling II functional response is introduced. Based on the comparison theorem, sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained. An example is also presented to illustrate our main results.

scholarly journals Mathematical analysis of an influenza A epidemic model with discrete delay

2017 ◽  
Vol 324 ◽  
pp. 155-172 ◽  
Author(s):  
P. Krishnapriya ◽  
M. Pitchaimani ◽  
Tarynn M. Witten
Keyword(s):  
Mathematical Analysis ◽  
Epidemic Model ◽  
Influenza A ◽  
Discrete Delay

Predator-dependent functional responses and interaction strengths in a natural food web

2004 ◽  
Vol 61 (11) ◽  
pp. 2215-2226 ◽  
Author(s):  
Timothy E Essington ◽  
Sture Hansson
Keyword(s):  
Food Webs ◽  
Functional Response ◽  
Gadus Morhua ◽  
Prey Species ◽  
Clupea Harengus ◽  
Natural Food ◽  
Functional Responses ◽  
Predation Mortality ◽  
Highly Sensitive ◽  
Predator Abundance

Predator-dependent functional responses decouple predation mortality from fluctuations in predator abundance and therefore can prevent strong "top-down" interaction strengths in food webs. We evaluated whether contrasts in the functional response of Baltic Sea cod (Gadus morhua) were consistent with the contrasting population dynamics of two prey species, herring (Clupea harengus) and sprat (Sprattus sprattus): sprat abundance increased nearly threefold following a sharp decline in the cod population (a strong interaction), whereas herring abundance failed to increase (a weak interaction). We found striking differences in the functional response of cod on alternative prey, and these were consistent with the observed patterns in interaction strengths. Cod predation was the dominant source of mortality for age-1 and age-2 sprat but was only important for age-1 herring. Moreover, the magnitude of predation mortality on age-1 and age-2 sprat was highly sensitive to cod biomass, whereas predation mortality on herring was only moderately sensitive to cod biomass. These analyses suggest the possibility that food webs are comprised of linkages that vary with respect to the magnitude and importance of predation mortality and how this mortality varies with changes in predator abundance.

scholarly journals Mathematical analysis of an age structured heroin-cocaine epidemic model

2017 ◽  
Vol 22 (11) ◽  
pp. 0-0
Author(s):  
Abdennasser Chekroun ◽  
◽  
Mohammed Nor Frioui ◽  
Toshikazu Kuniya ◽  
Tarik Mohammed Touaoula ◽  
...  
Keyword(s):  
Mathematical Analysis ◽  
Epidemic Model ◽  
Age Structured

scholarly journals Derivation of predator functional responses using a mechanistic approach in a natural system

2020 ◽  
Author(s):  
Andréanne Beardsell ◽  
Dominique Gravel ◽  
Dominique Berteaux ◽  
Gilles Gauthier ◽  
Jeanne Clermont ◽  
...  
Keyword(s):  
Functional Response ◽  
Prey Species ◽  
Mechanistic Model ◽  
Natural System ◽  
Field Observations ◽  
Functional Responses ◽  
Acquisition Rate ◽  
Predator Prey ◽  
Mechanistic Approach ◽  
Acquisition Rates

AbstractThe functional response is central to our understanding of any predator–prey system as it establishes the link between trophic levels. Most functional responses are evaluated using phenomenological models linking predator acquisition rate and prey density. However, our ability to measure functional responses using such an approach is often limited in natural systems and the use of inaccurate functions can profoundly affect the outcomes of population and community models. Here, we develop a mechanistic model based on extensive data to assess the functional response of a generalist predator, the arctic fox (Vulpes lagopus), to various tundra prey species (lemmings and the nests of geese, passerines and sandpipers). We found that predator acquisition rates derived from the mechanistic model were consistent with field observations. Although sigmoidal functional responses were previously used to model fox-prey population dynamics, none of our simulations resulted in a saturating response in all prey species. Our results highlight the importance of predator searching components in predator-prey interactions, especially predator speed, while predator acquisition rates were not limited by handling processes. By combining theory with field observations, our study provides evidences that predator acquisition rate is not systematically limited at the highest prey densities observed in a natural system. We reinforce the idea that functional response categories, typically types I, II, and III, should be considered as particular cases along a continuum. Specific functions derived with a mechanistic approach for a range of densities observed in natural communities should improve our ability to model and understand predator-prey systems.

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