Sains Malaysiana 43(7)(2014): 1045–1051

Effect of Predators on the Spread of Hantavirus Infection

(Kesan Pemangsa ke atas Penyebaran Jangkitan Hantavirus)

F.M. YUSOF*, A.I.B. MD. ISMAIL & N.M. ALI

School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia

Received: 6 November 2012/Accepted: 16 September 2013

ABSTRACT

Hantavirus is a serious disease caused by rodents which can lead to mortality. Many efforts have been carried out by researchers to develop and analyze mathematical models of Hantavirus infection. In this paper, the Peixoto and Abramson (2006) biodiversity model is modified to include the effect of predators and study the prediction of the modified model. When rodent and predator populations are in competition, the predator populations have the effect of reducing the prevalence of infection. Predators may be used for control and reduces the number of competing species to stabilize the populations at a persistent equilibrium.

Keywords: Biodiversity model; competition dynamics; Hantavirus infection; mathematical model; predator-prey model

ABSTRAK

Hantavirus adalah jangkitan serius yang disebabkan oleh tikus yang boleh membawa kepada kematian. Banyak usaha yang telah dilakukan oleh para penyelidik untuk membangun dan mengalisis model matematik jangkitan Hantavirus. Dalam artikel ini, model biodiversiti Peixoto dan Abramson (2006) diubahsuai untuk memasukkan kesan pemangsa dan mengkaji ramalan model. Apabila populasi tikus dan pemangsa dalam persaingan, populasi pemangsa memberi kesan pengurangan kekerapan jangkitan tikus. Pemangsa boleh digunakan untuk mengawal dan mengurangkan bilangan spesies yang bersaing untuk menstabilkan populasi pada keseimbangan yang berterusan.

Kata kunci: Jangkitan Hantavirus; model biodiversiti; model matematik; model pemangsa-mangsa; persaingan dinamik

REFERENCES

Abdul Karim, M.F., Ismail, A.I. & Ching, H.B. 2009. Cellular automata modeling of hantavirus infection. Chaos, Solitons & Fractals 41(5): 2847-2853.

Abramson, G. & Kenkre, V.M. 2002. Spatiotemporal patterns in the hantavirus infection. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 66(1): 011912-1-5.

Abramson, G., Kenkre, V.M., Yates, T.L. & Parmenter, B.R. 2003. Traveling waves of infection in the Hantavirus epidemics. Bulletin of Mathematical Biology 65(3): 519-534.

Campbell, N.A., Reece, J.B., Urry, L.A., Cain, M.L., Wasserman, S.A., Minorsky, P.V. & Jackson, R.B. 2008. Biology. 8th ed. San Francisco: Pearson Education, Inc.

Giuggioli, L., Kenkre, V.M., Abramson, G. & Camelo-Neto, G. 2006. Theory of hantavirus infection spread incorporating localized adult and itinerant juvenile mice. European Physical Journal B 55(4): 461- 470.

Gui, Z. & Ge, W. 2005. The effect of harvesting on a predator-prey system with stage structure. Ecological Modelling 187(2-3): 329-340.

Goh, S.M., Ismail, A.I.M., Noorani, M.S.M. & Hashim, I. 2009. Dynamics of the hantavirus infection through variational iteration method (VIM). Nonlinear Analysis: Real World Applications 10(4): 2171-2176.

Kenkre, V.M., Giuggioli, L., Abramson, G. & Camelo-Neto, G. 2007. Theory of hantavirus infection spread incorporating localized adult and itinerant juvenile rodents. European Physical Journal B 55(4): 461-470.

Ostfeld, R.S. & Holt, R.D. 2004. Are predators good for your health? Evaluating evidence for top-down regulation of zoonotic disease reservoirs. Frontiers in Ecology Environment 2(1): 13-20.

Peixotu, I.D. & Abramson, G. 2006. The effect of biodiversity on the hantavirus epizootic. Ecology 87(4): 873-879.

Rafikov, M., Balthazar, J.M. & Von Bremen, H.F. 2008. Mathematical modeling and control of population systems: Applications in biological pest control. Applied Mathematics and Computation 200(2): 557-573.

Schurr, A. 2003. Monte-Carlo simulation of the predator/ prey model. (Online) http: // www.trincoll.edu / ~pbrown / MathModeling/ Student Projects /PreditorPray/predprey. htm. Accessed on 1 February 2012.

Smith, T.M. & Smith, R.L. 2009. Elements of Ecology. 7th ed. San Francisco: Pearson Education, Inc.

Yusof, F.M., Ismail, A.I.M. & Ali, N.M. 2010. Modeling population harvesting of rodents for the control of hantavirus infection. Sains Malaysiana 39(6): 935-940.

*Corresponding author; email: fauzikmk@hotmail.com