Modeling of the Dengue Outbreak Using Modified SEIR Model in Jaffna District

Abstract

Dengue fever is a mosquito-borne viral disease transmitted to humans through the bite of infected Aedes mosquitoes, mostly Aedes aegypti. In the Jaffna District, about 200 cases of dengue fever per 100,000 people in 2019 was reported. A better understanding of the transmission dynamics of the dengue disease epidemic in Jaffna is vital for public health. Mathematical modeling is a useful technique for analysing transmission dynamics. This research aims to improve the theoretical understanding of dengue transmission through a simulation and the related changes in the dengue epidemic in the Jaffna District. The four-compartment (susceptible (𝑆ℎ), exposed (𝐸ℎ), infected (𝐼ℎ), and removed (𝑅ℎ)(SEIR)) models for human and two compartment (susceptible (𝑆𝑣), exposed (𝐸ℎ),and infected(𝐼𝑣))model for vectors with seven nonlinear differential equations were used to formulate a mathematicalmodel. Relevant data from 2019were collected from Jaffna regional health authorities and analysed with the developed model. Two equilibrium points were found: the first point was locally asymptotically stable, and the other was focus asymptotically stable. Moreover, the reproduction number 𝑅0>1. The proposed model shows that the focus of dengue fever would be stable in the Jaffna District except in some specific places