Sains Malaysiana 39(6)(2010): 935–940

Modeling Population Harvesting of Rodents for the Control of Hantavirus Infection

(Pemodelan Proses Populasi Penuaian Tikus bagi Mengawal Jangkitan Hantavirus)

F.M.Yusof*, A.I.B. Md. Ismail & N.H.M. Ali

School of Mathematical Sciences

Universiti Sains Malaysia, 11800 USM, Penang, Malaysia

Received: 17 November 2009 / Accepted: 21 May 2010

ABSTRACT

Hantaviruses are infectious agents that can cause diseases resulting in deaths in humans and are hosted by rodents without affecting the hosts themselves. A simple mathematical model describing the spread of the Hantavirus infection in rodents has been proposed and developed by Abramson and Kenkre where the model takes into account the temporal and spatial characteristics of this infection. In this paper, we extended this model to include the process of harvesting and study the impact of different harvesting strategies in the spread of the Hantavirus infection in rodents. Several numerical simulations were carried out and the results are discussed.

Keywords: Hantavirus; harvesting; mathematical model; numerical simulations

ABSTRAK

Hantavirus adalah ejen jangkitan penyakit yang boleh menyebabkan kematian di kalangan manusia dan berperumahkan tikus tanpa memberi kesan kepada perumah itu sendiri. Model matematik mudah yang menjelaskan pembiakan jangkitan hantavirus ke atas tikus telah dicadang dan dibangunkan oleh Abramson dan Kenkre dengan model tersebut mengambilkira ciri ruang dan masa jangkitan ini. Dalam makalah ini, kami meluaskan model ini dengan memasukkan proses penuaian dan mengkaji kesan strategi penuaian yang berbeza ke atas pembiakan jangkitan hantavirus ke atas tikus. Beberapa simulasi berangka telah dijalankan dan keputusan dibincangkan.

Kata kunci: Hantavirus; penuaian; model matematik; simulasi berangka

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 66: 011912-1-5.

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

Bairagi, N., Chaudhuri, S. & Chattopadhyay, J. 2009. Harvesting as a disease control measure in an eco-epidemiological system - A theoretical study, Mathematical Biosciences 217(2): 134-144.

Cross, A., McGuire, G. & Tashian, C. 1998. Logistic growth with harvesting (Online) Available: http://tashian.com/carl/docs/harvesting/ (accessed 27 April 2006).

Giuggioli, L., Kenkre, V.M., Abramson, G. & Camelo-Neto, G. 2006. Theory of hantavirus infection spread incorporating localized adult and itinerant juvenile mice, Eur. Phys. Jour. B 55: 461-470.

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.

Hjelle, B. 2007. Pathogenesis of hantavirus infection. (Online) Available: http:// patients.uptodate.com/topic.asp?file=viral_in/24412 (accessed June 2007).

Idels, L.V. & Wang, M. 2008. Harvesting fisheries management strategies with modified effort function, International Journal of Modelling, Identification and Control 3(1): 83-87.

Matsuoka, T. & Seno, H. 2008. Ecological balance in the native population dynamics may cause the paradox of pest control with harvesting, Journal of Theoretical Biology 252(1): 87-97.

Miner, R. & Wicklin, F. 1996. Modeling population growth: harvesting. (Online) Available: http://www.geom.uiuc.edu/education /calc-init /population /harvest.html (accessed 24 June 2007).

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

*Corresponding author; email: fauzikmk@hotmail.com