Journal Article

Optimal‐Control Techniques for Managing Dengue Outbreaks: An Advanced Mathematical Modeling

Hossain, Md. Shamim, Hye, Md. Abdul, Rahman, Md. Mizanur, Miah, Md. Sajib

2025

Overview

Dengue remains a major public health threat in tropical and subtropical regions. We develop a general human–vector SEIR–SEI optimal‐control framework that integrates four time‐dependent interventions: public awareness/behavioral protection, u1(t) ${{u}_1}( t )$ , enhanced clinical management u2(t) ${{u}_2}( t )$ , adulticide spraying u3(t) ${{u}_3}( t )$ , and larval‐source reduction/larvicide u4(t) ${{u}_4}( t )$ . The controls act by reducing effective human–vector contact, increasing human recovery, increasing adult mosquito mortality, and suppressing vector recruitment, respectively. The objective is to minimize a weighted sum of infectious burden in humans and vectors and the quadratic costs of implementation over a finite horizon, subject to epidemiological dynamics and standard control bounds 0 ≤ ui (t) ≤ 1. Using Pontryagin's Maximum Principle, we derive the necessary conditions for optimality and solve the resulting two‐point boundary value problem numerically. Numerical simulations conducted in MATLAB, calibrated with real data from Bangladesh, perform uncertainty and sensitivity analyses around the basic reproduction number and key transmission, and control parameters reveal that Strategy‐4, which includes public awareness, treatment, and insecticide spraying (u1(t)≠0,u2(t)≠0,u3(t)≠0,u4(t)=0 ${{u}_1}( t ) \\ne 0,\\ {{u}_2}( t ) \\ne 0,\\ {{u}_3}( t ) \\ne 0,{{u}_4}( t ) = 0$ ), is the most effective and cost‐efficient approach. This strategy reduces the time to disease elimination from over 100 days to approximately 74.7 days, achieving a 72.66% faster reduction than natural decay. The findings demonstrate that the proposed control strategies can significantly curb the progression of dengue and support targeted public health interventions to manage outbreaks effectively.

• Publisher: John Wiley & Sons, Inc,Wiley-VCH
• Subject: Adulticides / basic reproduction number / Boundary value problems / Costs / dengue disease / Dengue fever / Disease / Epidemics / Epidemiology / Health promotion / Health risks / Immunity (Disease) / Infections / Insecticides / local and global stability / Mathematical models / Mortality / Mosquitoes / numerical simulation / optimal‐control strategies / Optimization / Outbreaks / Pontryagin principle / Public awareness / Public health / Sensitivity analysis / Spraying / Time dependence / Vector-borne diseases / Vectors