Sains Malaysiana 49(5)(2020): 1191-1200

http://dx.doi.org/10.17576/jsm-2020-4905-24

Mathematical Model of Dengue Virus with Predator-Prey Interactions

 (Model Matematik Virus Denggi dengan Interaksi Pemangsa-Mangsa)

SARINAH BANU MOHAMED SIDDIK¹*, FARAH AINI ABDULLAH² & AHMAD IZANI MD. ISMAIL²

¹Institute of Engineering Mathematics, Universiti Malaysia Perlis, 02600 Arau, Perlis, Malaysia

²School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM Pulau Pinang, Malaysia

Received: 8 August 2019/Accepted: 15 January 2020

ABSTRACT

In this paper, a mathematical model of dengue incorporating two sub-models that: describes the linked dynamics between predator-prey of mosquitoes at the larval stage, and describes the dengue spread between humans and adult mosquitoes, is formulated to simulate the dynamics of dengue spread. The effect of predator-prey dynamics in controlling the dengue disease at the larval stage of mosquito populations is investigated. Stability analysis of the equilibrium points are carried out. Numerical simulations results indicate that the use of predator-prey dynamics of mosquitoes at the larval stage as biological control agents for controlling the larval stage of dengue mosquito assists in combating dengue virus contagion.

Keywords: Dengue virus; endemic equilibrium; numerical simulation; predator-prey

ABSTRAK

Dalam kertas ini, satu model matematik denggi yang menggabungkan dua sub-model iaitu: menerangkan dinamik antara nyamuk  pemangsa-mangsa  pada peringkat jejentik dan menerangkan penyebaran denggi antara manusia dan nyamuk dewasa, diformulasikan untuk mensimulasi dinamik penyebaran denggi.  Kesan dinamik pemangsa-mangsa untuk mengawal penyakit denggi pada peringkat jejentik populasi nyamuk diselidik. Analisis kestabilan titik kesimbangan dijalankan. Simulasi berangka menunjukkan bahawa penggunaan dinamik pemangsa-mangsa nyamuk pada peringkat jejentik sebagai agen kawalan biologi untuk mengawal tahap jejentik nyamuk denggi membantu dalam memerangi penularan virus denggi.

Kata kunci: Keseimbangan endemik; pemangsa-mangsa; simulasi berangka; virus denggi

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*Corresponding author; email: sarinah@unimap.edu.my