Disease dynamics and optimal control strategies of a two serotypes dengue model with co-infection

This paper aims to explore stability and bifurcations with control analysis of a co-infected two serotypes dengue model in presence of three controls, namely protection control, treatment control and mosquito killing efforts. First we analyze the model incorporating with constant controls then find the control path considering variable control. We examine biological feasibility of the considered model along with existence and stability criteria of different equilibrium with respect to basic reproduction number. Stability of serotype-I, serotype-II free equilibrium and positive co-existence equilibrium are investigated. Center manifold theorem is used to prove the stability of the co-infected endemic equilibrium. The model experiences Transcritical bifurcation with respect to basic reproduction number. Sensitivity analysis has been employed to identify most influential model parameters to control the infection. The time dependent optimal control problem is solved analytically and numerically using Pontryagin's maximum principle. At last efficiency analysis has been carried out to find out more suitable control to combat the dengue disease. It is established from the analysis, protection control with treatment is more powerful than mosquito killing efforts by humans with treatment for controlling dengue. (c) 2023 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.