Title: The nonlinear dynamics of the dengue mosquito reproduction with respect to climate in urban Colombo: a discrete time density dependent fuzzy model

Authors: W.P.T.M. Wickramaarachchi; S.S.N. Perera

Addresses: Department of Mathematics and Computer Science, The Open University of Sri Lanka, Nawala, Nugegoda, Sri Lanka ' Research and Development Center for Mathematical Modeling, Faculty of Science, University of Colombo, Colombo 03, Sri Lanka

Abstract: Dengue has been a major public health concern in most parts of the tropical world and the dynamics of dengue disease transmission is complex due to several external factors. Various mathematical models have been developed to understand the transmission dynamic of the dengue disease. However, the fixed parameter values have been used in those models so the real dynamics of the transmission is not explained completely. Mosquito density is responsible for the transmission of dengue locally, whilst human mobility causes transmission of the disease globally. Thus mosquito density is a vital parameter for study the dengue transmission which depends heavily on climate, geography and human behaviour. In this study, the density dependent Gompertz model with climate variation factor is used to model the mosquito density. Various levels of climate factor combinations act differently on the dynamics of mosquito density. Thus modelling the climate effect to grow mosquito populations should be done under uncertainty. The fuzzy membership functions are constructed for each factor rainfall and temperature where the membership value in [0, 1] explains the degree of favorability to mosquitoes from each factor in different levels. The Modified Einstein Sum operator is used to compute the overall measure of unfavorability from these two climate factors. The standardised mosquito density and real risk of dengue are compared using urban Colombo data and defining a mapping function. It is noted that 94.77% of data points are able to determine the real dengue risk 90% accurately.

Keywords: climate; dengue; fuzzy logic; mosquito density; SIR models.

DOI: 10.1504/IJMMNO.2017.086802

International Journal of Mathematical Modelling and Numerical Optimisation, 2017 Vol.8 No.2, pp.145 - 161

Received: 20 Jul 2016
Accepted: 01 May 2017
Published online: 26 Sep 2017 *

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