# Optimal control of non-autonomous SEIRS models with vaccination and treatment

## TL;DR

This paper investigates optimal control strategies for a non-autonomous SEIRS epidemic model incorporating vaccination and treatment, providing theoretical existence results and simulation comparisons between autonomous and periodic models.

## Contribution

It introduces a novel optimal control framework for non-autonomous SEIRS models with general incidence functions, including existence, uniqueness, and simulation analysis.

## Key findings

- Existence and uniqueness of optimal control solutions established.
- Simulation results compare autonomous and periodic models.
- Controlled models show improved epidemic outcomes.

## Abstract

We study an optimal control problem for a non-autonomous SEIRS model with incidence given by a general function of the infective, the susceptible and the total population, and with vaccination and treatment as control variables. We prove existence and uniqueness results for our problem and, for the case of mass-action incidence, we present some simulation results designed to compare an autonomous and corresponding periodic model, as well as the controlled versus uncontrolled models.