# Optimal Vaccination and Treatment Schedules in a Deterministic Avian influenza Model

## Authors

• Nuning Nuraini Department of Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha 10, Bandung 40132, Indonesia
• Tasmi Tasmi Department of Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha 10, Bandung 40132, Indonesia

## Keywords:

genetic algorithm, host-vector model, medical treatment, optimization, vaccination,

## Abstract

In this study, a transmission model of the Avian influenza disease was developed and analyzedin view of optimization of vaccination and medical treatment. The model is a host-vector model. We focussed on control of Avian influenza, where a vaccination is given to susceptible poultry, while medical treatment is given to infected humans. In the model, the human population is divided into four compartments: susceptible humans, infected humans, recovered humans, and treated humans. Meanwhile, the poultry population is divided into three compartments: susceptible poultry, infected poultry, and vaccinated poultry. To analyze the dynamical behavior of the model, we obtained the disease-free equilibrium, the endemic equilibrium, and the basic reproduction ratio.Furthermore, a model of the optimal vaccination and medical treatment schedule was constructed to know the optimal strategy for controlling Avian influenza. The model can be used to determine the minimal cost of controlling the disease. The model is solved by a genetic algorithm method. Numerical simulations showed that effective control of Avian influenza can be achieved with a combination of vaccination and medical treatment. Likewise, the optimal schedule and strategy for controlling Avian influenza are shown.

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