Dynamics of Infected Predator-Prey System with Nonlinear Incidence Rate and Prey in Refuge

A predator-prey system with nonlinear incidence rate and refuging in prey is proposed to describe behavior change of certain infected diseases on healthy prey when the number of infected prey is getting large, while predator can predate prey by accessing refuging in prey. Therefore, this paper discu...

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Autor principal:	Adin Lazuardy Firdiansyah
Formato:	article
Lenguaje:	EN
Publicado:	Department of Mathematics, UIN Sunan Ampel Surabaya 2020
Materias:	predator-prey system; nonlinear incidence rate; refuge; stability Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/9819c8c9570f470f8c3b3bd9ad07a3f7
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spelling	oai:doaj.org-article:9819c8c9570f470f8c3b3bd9ad07a3f72021-12-02T15:03:51ZDynamics of Infected Predator-Prey System with Nonlinear Incidence Rate and Prey in Refuge2527-31592527-316710.15642/mantik.2020.6.2.123-134https://doaj.org/article/9819c8c9570f470f8c3b3bd9ad07a3f72020-10-01T00:00:00Zhttp://jurnalsaintek.uinsby.ac.id/index.php/mantik/article/view/972https://doaj.org/toc/2527-3159https://doaj.org/toc/2527-3167A predator-prey system with nonlinear incidence rate and refuging in prey is proposed to describe behavior change of certain infected diseases on healthy prey when the number of infected prey is getting large, while predator can predate prey by accessing refuging in prey. Therefore, this paper discusses the dynamics behavior predator-prey model with the spread of infected disease that is denoted by nonlinear incidence rate and adding prey refuge. We find the existence of eight non-negative equilibrium in the model, which their local stability has been determined. Furthermore, we also observe the prey refuge properties in the model. We find that prey refuge can prevent extinction in prey populations. In the end, some numerical solutions are carried out to illustrate our analytic results. For future work, we can investigate the harvesting effect in both populations, which is disease control in the predator-prey model with the spread of infected disease.Adin Lazuardy FirdiansyahDepartment of Mathematics, UIN Sunan Ampel Surabayaarticlepredator-prey system; nonlinear incidence rate; refuge; stabilityMathematicsQA1-939ENMantik: Jurnal Matematika, Vol 6, Iss 2, Pp 123-134 (2020)
institution	DOAJ
collection	DOAJ
language	EN
topic	predator-prey system; nonlinear incidence rate; refuge; stability Mathematics QA1-939
spellingShingle	predator-prey system; nonlinear incidence rate; refuge; stability Mathematics QA1-939 Adin Lazuardy Firdiansyah Dynamics of Infected Predator-Prey System with Nonlinear Incidence Rate and Prey in Refuge
description	A predator-prey system with nonlinear incidence rate and refuging in prey is proposed to describe behavior change of certain infected diseases on healthy prey when the number of infected prey is getting large, while predator can predate prey by accessing refuging in prey. Therefore, this paper discusses the dynamics behavior predator-prey model with the spread of infected disease that is denoted by nonlinear incidence rate and adding prey refuge. We find the existence of eight non-negative equilibrium in the model, which their local stability has been determined. Furthermore, we also observe the prey refuge properties in the model. We find that prey refuge can prevent extinction in prey populations. In the end, some numerical solutions are carried out to illustrate our analytic results. For future work, we can investigate the harvesting effect in both populations, which is disease control in the predator-prey model with the spread of infected disease.
format	article
author	Adin Lazuardy Firdiansyah
author_facet	Adin Lazuardy Firdiansyah
author_sort	Adin Lazuardy Firdiansyah
title	Dynamics of Infected Predator-Prey System with Nonlinear Incidence Rate and Prey in Refuge
title_short	Dynamics of Infected Predator-Prey System with Nonlinear Incidence Rate and Prey in Refuge
title_full	Dynamics of Infected Predator-Prey System with Nonlinear Incidence Rate and Prey in Refuge
title_fullStr	Dynamics of Infected Predator-Prey System with Nonlinear Incidence Rate and Prey in Refuge
title_full_unstemmed	Dynamics of Infected Predator-Prey System with Nonlinear Incidence Rate and Prey in Refuge
title_sort	dynamics of infected predator-prey system with nonlinear incidence rate and prey in refuge
publisher	Department of Mathematics, UIN Sunan Ampel Surabaya
publishDate	2020
url	https://doaj.org/article/9819c8c9570f470f8c3b3bd9ad07a3f7
work_keys_str_mv	AT adinlazuardyfirdiansyah dynamicsofinfectedpredatorpreysystemwithnonlinearincidencerateandpreyinrefuge
_version_	1718389030556532736

Dynamics of Infected Predator-Prey System with Nonlinear Incidence Rate and Prey in Refuge

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