A mathematical model with control to analyse the dynamics of dengue disease transmission in urban Colombo

Abstract

Dengue is a mosquito-borne disease. It has been an important public health problem particularly in the tropical and sub-tropical regions in the world, for which no vaccine or successful treatment has been found. Therefore, prevention and control play a vital role in minimising the risk of dengue in vulnerable populations. Various mathematical models such as the SIR model have been developed to understand the transmission dynamics of dengue. The main drawback of these dynamic models is the lack of predictability with respect to external factors such as climate, geography, demography and human behaviour due to usage of fixed parameters. The mosquito density, which depends heavily on various external factors such as climate is a critical parameter of these models and is responsible for the local transmission of the disease. In this study, the mosquito density is modelled with respect to changing levels of climate favourable for mosquito reproduction. A climate risk index developed using fuzzy set theory is used to vary the mosquito density with respect to rainfall and temperature and this measure is included in the SIR model. Finally, two measures, u1 and u2 are introduced to control adult mosquitoes and growing juveniles using two methods. The first method is theoretical where we consider u1 and u2 as random processes from uniform distribution. The second method involves continuous and constant control measures over time. The numerical results of the SIR model sussest that the dynamics of infections has changed and the number of infections is reduced as the efficiency of the control measures increase.