A dynamic S-I-P model with disease in the prey population and holling type II functional response

K. Ni’mah; S.B. Waluya; M. Kharis

doi:10.17654/MS100050727

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A dynamic S-I-P model with disease in the prey population and holling type II functional response

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K. Ni’mah, S.B. Waluya, M. Kharis

2016 Far East Journal of Mathematical Sciences Vol. 100 Issue 5 Article Cited by 0 SDG 14

Abstract

In this paper, a modified S-I-P of two species predator-prey interactions model is discussed. The S-I-P system consists of three differential equations that represent sub-populations growth of susceptible-preys (S), infected-preys (I) and predators (P). In prey population there is deadly disease transmission rated with Holling type II response characteristic of predator to catched prey. The analysis result showed that the system has six equilibrium points. There are always two points which are unstable in any condition. Routh-Hurwitz criteria are used to analyze the stability of the equilibrium points. Numerical simulations are carried out to demonstrate the results obtained. © 2016 Pushpa Publishing House, Allahabad, India.

Affiliations

Department of Mathematics, Semarang State University, Semarang, 50299, Indonesia

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