Optimal control  of  a vector-host epidemics model

Qingkai Kong; Zhipeng Qiu; Zi Sang; Yun Zou

doi:10.3934/mcrf.2011.1.493

Article Contents

2011, Volume 1, Issue 4: 493-508. Doi: 10.3934/mcrf.2011.1.493

This issue Previous Article Time-delayed boundary feedback stabilization of the isothermal Euler equations with friction Next Article Inverse source problem with a final overdetermination for a fractional diffusion equation

Optimal control of a vector-host epidemics model

1.
School of Automation, Nanjing University of Science and Technology, Nanjing, 210094
2.
Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing, 210094

Received: June 2011

Revised: September 2011

Published: December 2011

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Abstract

In this paper, a vector-host epidemic model with control measures is considered to assess the impact of control measures on the prevalence of the vector-host diseases. We incorporated mosquito-reduction strategy and host medical treatment into the model. For the basic vector-host model, we provide sufficient conditions for the local stability of the disease free equilibrium (DFE) and the sensitivity analysis for the reproduction number with respect to the model parameters. Using the optimal control theory, the optimal levels of the two controls are characterized, and then the existence and uniqueness for the optimal control pair are established. Numerical simulations are further conducted to confirm and extend the analytical results. Numerical results suggest that optimal multi-control strategy is a more beneficial choice in fighting the outbreak of vector-host diseases. For the vector-host epidemics, vector control measures should be taken prior to other measures.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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