Optimal control of a dengue epidemic model with vaccination

We present a SIR+ASI epidemic model to describe the interaction between human and dengue fever mosquito populations. A control strategy in the form of vaccination, to decrease the number of infected individuals, is used. An optimal control approach is applied in order to find the best way to fight the disease.

💡 Research Summary

The paper presents a mathematical framework for controlling dengue fever through vaccination, using an SIR‑ASI model that captures the dynamics of both human hosts and mosquito vectors. Humans are divided into susceptible (S_h), infected (I_h), and recovered (R_h) compartments, while mosquitoes are represented by an aquatic stage (A_m) and adult susceptible (S_m) and infected (I_m) classes. The model consists of six coupled ordinary differential equations that incorporate natural birth and death rates, mosquito biting frequency (B), transmission probabilities (β_mh, β_hm), and the maturation rate from aquatic to adult mosquitoes (η_A).

Vaccination is introduced as a time‑dependent control variable u(t) bounded between 0 and 1, with an efficacy reduction factor σ (σ = 0 corresponds to a perfect vaccine, σ = 1 to a completely ineffective one). The objective functional to be minimized is

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