Optimal control and cost-effectiveness analysis for dengue fever model with asymptomatic and partial immune individuals

Abstract

Dengue is a vector-borne disease with an increasing incidence worldwide, and it is transmitted by the bites of mosquitoes infected with dengue viruses. This viral infection persistently affects economic sectors and public health. Hence, this paper analyzes an optimal control model of dengue infection with partial immune and asymptomatic individuals. We introduced four time-dependent control measures, thus treated bednets, treatment (prophylactics), insecticides, and vaccination. There is a threshold parameter RC; when RC is less than or equal to one, the disease-free equilibrium exists, and when RC is greater than one, the endemic equilibrium exists. The equilibrium points are globally asymptotically stable using Lyapunov functions. We notice that the control reproduction number, RC, is dependent on the initial number of mosquito population, Nv0, and that of the initial human population, Nh0. It is also noticed that, RC increases whenever Nv0 increases, with constant Nh0. We obtain the adjoint system of the proposed optimal control problem. The optimized system is then solved numerically using Runge–Kutta fourth-order scheme. We performed a cost-effectiveness analysis by proposing five strategies for the optimal control problem. We then calculated the efficacy ratio (ER), infection averted ratio (IAR), average cost-effectiveness ratio (ACER), and the incremental cost-effectiveness ratio (ICER). These results show that the use of vaccination and treatment has the least incremental cost-effectiveness ratio and is consequently more cost-effective (cost-saving). However, in terms of infection averted, the combined use of treated bednets, vaccination, treatment, and insecticides is just as good as vaccination and treatment only.