Cost-Effective Optimal Control Analysis To Co-Infection Model Of Dengue Fever And Typhoid Fever

Abstract

This study deals with the application of mathematical modeling in analyzing the transmission dynamics of diseases. In particular we develop an algebraic model that describes the interaction between two common diseases, namely dengue and typhoid fevers. To realistically describe the interdependence among agents that influence the spread of both diseases, we consider an environment of three populations: vector, human, and bacteria, which in total consist of ten compartments. In order to be able to intervene the system, we equip the model with four control variables, namely mosquito eradication, the use of mosquito repellent, treatment of individuals carrying and infected with typhoid, and education on healthy living. The well-known Pontryagin maximum principle was carried out in deriving necessary conditions for optimal controls and the so-called forward-backward sweep method combining with the fourth order Runge-Kutta algorithm was utilized in the implementation of numerical solutions. A series of control scenarios were evaluated based on their benefits obtained and costs incurred. An ACER and ICER based cost effectiveness analysis was conducted to characterize the best control strategy. In a case study with 1000 human populations, it is suggested that a strategy with all control alternatives provides the most effective results.