Optimal control strategies for an age‐structured SEIR epidemic model

Abstract

We formulate an age-structured SEIR epidemic model using vaccination and treatment as control measures. Using the method of characteristics and fixed point arguments, we prove the existence of a unique positive solution to our proposed nonlinear model. We use a suitable objective functional and prove the existence of optimal control variables. Depending on the nature of the problem, the necessary conditions for the optimal control problem are established using the maximum principle of Pontryagin's type. Tools of control theory are used for obtaining optimal control characterizations in terms of state and adjoint variables. To illustrate theoretical results, parameter values are chosen to simulate both with and without control problems. Numerical findings reveal that when, where, and to whom control measures should be implemented for best results of a control program.

Dynamical analysis and optimal control of an age‐structured epidemic model with asymptomatic infection and multiple transmission pathways

“…The proof of Theorem 6 is similar to Theorem 3.1 in Khan and Zaman [38]; it is omitted here. Assume that there exists another set of control variables u 𝜖 1 (t, a) = u 1 (t, a) + 𝜖h 1 (t, a) and u 𝜖 2 (t, b) = u 2 (t, b) + 𝜖h 2 (t, b), where h 1 (t, a) and h 2 (t, b) are variation functions and 𝜖 ∈ (0, 1).…”

“…Wang et al [37] proposed and investigated the global dynamics in a Malaria model with age structure, discussed optimal control existence, as well as suggested effective measures to control Malaria transmission. Khan and Zaman [38] developed an age-structured susceptible-exposed-infected-removed (SEIR) infectious disease model with vaccination and treatment as control measures and obtained the necessary conditions for the optimal control problem by applying the maximum principle of Pontryagin type. For more related researches, see previous studies [39][40][41][42][43][44].…”