Modeling optimal vaccination strategy for dengue epidemic model: a case study of India

Abstract

Dengue fever is a mosquito-borne infectious disease which is transmitted through Aedes aegypti mosquitoes. It is one of the major global health issues in the tropical and subtropical regions of the world. Its dynamics are very complicated owing to the coupling among multiple transmission pathways and various components in pathogen. Due to absence of proper medicine or vaccination, mathematical modeling plays an important role in understanding the disease dynamics and in designing strategies to control the spread of dengue virus. In this paper, we studied a non-linear vector-host model to investigate the transmission dynamics of dengue virus which can be controlled by vaccination as well as treatment. Analysis of model start with the basic reproduction number , when it is less than one, the system become locally asymptotically stable about the virus-free equilibrium point. We calibrated our proposed model corresponding to transmission of dengue virus using real data for six Indian states, namely Tamil Nadu, Kerala, Delhi, Gujarat, Rajasthan and Karnataka by using the least square method. Moreover, we performed normalized forward sensitivity analysis of the basic reproduction number and obtained that mitigating the disease transmission rate of mosquito and human population is the most important factor in achieving dengue control. Finally, an objective functional has been developed to minimize the cost of the vaccination and solved with the aid of the Pontryagin’s Maximum Principle. The implementation of the optimal treatment policy shows a significant reduction of the hospitalized individuals as well as infected individuals. We then performed extensive numerical simulations to validate our theoretical analysis with aid of the estimated model parameters.