A mathematical study of an eco-epidemiological system on disease persistence and extinction perspective

Chakraborty, Kunal; Das, Kunal; Haldar, Samadyuti; Kar, Tapan Kumar

doi:10.1016/j.amc.2014.12.109

Cited by 12 publications

(4 citation statements)

References 31 publications

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“…Corollary 2. If R ℓ P ER > 1 then the infective (I n ) is strongly persistent in system (2), where (x * n ) and (z * n ) are the components of the solution ((x * n , z * n )) in the periodic version of (13). Moreover, there exist a periodic orbit of period ω.…”

Section: 1mentioning

confidence: 99%

“…Lately, several works related to eco-epidemiological models have appeared in the literature. In [2], the authors study the extinction and persistence of the disease in some eco-epidemiological systems; in [1] the global stability of a delayed ecoepidemiological model with Holling type III functional response is addressed, and in [14] the authors study an eco-epidemiological model with harvesting.…”

Section: Introductionmentioning

confidence: 99%

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Dynamics of a discrete eco-epidemiological model with disease in the prey

Jesus¹,

Silva²,

Vilarinho³

2020

Preprint

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Using Mickens nonstandard method, we obtain a discrete family of nonautonomous eco-epidemiological models that include general functions corresponding to the predation of the infected and uninfected preys. We obtain results on the persistence and extinction of the infected preys assuming that the bi-dimensional predator-prey subsystem that describes the dynamics in the absence of the infection satisfies some assumptions. Some examples and simulations are undertaken to illustrate our results.

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Section: 1mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamics of a discrete eco-epidemiological model with disease in the prey

Jesus¹,

Silva²,

Vilarinho³

2020

Preprint

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“…There is already a large number of works concerning eco-epidemiological models. To mention just a few recent works, we refer [4] where a mathematical study on disease persistence and extinction is carried out; [5] where the authors study the global stability of a delayed eco-epidemiological model with holling type III functional response, and [2] where an eco-epidemiological model with harvesting is considered.…”

Section: Introductionmentioning

confidence: 99%

Periodic orbits for periodic eco-epidemiological systems with infected prey

Jesus¹,

Silva²,

Vilarinho³

2020

Preprint

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We address the existence of periodic orbits for periodic eco-epidemiological system with disease in the prey. To do it, we consider three main steps. Firstly we study a one parameter family of systems and obtain uniform bounds for the components of any periodic solution of these systems. Next, we make a suitable change of variables in our family of systems to establish the setting where we are able to apply Mawhin's continuation Theorem. Finally, we use Mawhin's continuation Theorem to obtain our result. Later on, we present two examples that include previous results in the literature and some numerical simulations to illustrate our results.Date: March 13, 2020. Key words and phrases. Eco-epidemiological system; periodic orbit; persistence. L. de Jesus, C. M. Silva and H. Vilarinho were partially supported by FCT through CMA-UBI (project UIDB/MAT/00212/2020).

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“…Sahoo assumed that, the interaction between predator and susceptible prey is of Holling type II functional response and that between predator and infected prey is of Holling type I functional response. In Chakraborty, Das, Haldar, and Kar (2015), Chakraborty et al proposed a predator-prey system with disease in prey and Holling CONTACT Zi Zhen Zhang zzzhaida@163.com type III functional response based on the work in Bhattacharyya and Mukhopadhyay (2011). Chakraborty et al studied a ratio-dependent eco-epidemiological system where prey population is subjected to harvesting (Chakraborty, Pal, & Bairagi, 2010).…”

Section: Introductionmentioning

confidence: 99%

Permanence and Hopf bifurcation of a delayed eco-epidemic model with Leslie–Gower Holling type III functional response

Zhang

Cao

Kundu

et al. 2019

Systems Science & Control Engineering

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This paper is concerned with a delayed eco-epidemic model with a Leslie-Gower Holling type III functional response. The main results are given in terms of permanence and Hopf bifurcation. First of all, sufficient conditions for permanence of the model are established. Directly afterward, sufficient conditions for local stability and existence of Hopf bifurcation are obtained by regarding the delay as bifurcation parameter. Finally, properties of the Hopf bifurcation are investigated with the aid of the normal form theory and centre manifold theorem. Numerical simulations are carried out to verify the obtained theoretical results.

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A mathematical study of an eco-epidemiological system on disease persistence and extinction perspective

Cited by 12 publications

References 31 publications

Dynamics of a discrete eco-epidemiological model with disease in the prey

Dynamics of a discrete eco-epidemiological model with disease in the prey

Periodic orbits for periodic eco-epidemiological systems with infected prey

Permanence and Hopf bifurcation of a delayed eco-epidemic model with Leslie–Gower Holling type III functional response

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