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Analysis of a simple influenza a (H1N1) model with optimal control
A.K. Srivastav,
Published in World Academic Union
2016
Volume: 12
   
Issue: 4
Pages: 307 - 319
Abstract
In this paper, a deterministic non-linear SEIHR type epidemic model for the transmission dynamics of Influenza A (H1N1) is proposed and analyzed. The existence and stability of different equilibria of this model are discussed in detail. The basic reproduction number R0 of the model is computed, and it is found that for R0 < 1, the disease free equilibrium of the model is globally stable. The endemic equilibrium exists only when R0 > 1, and is globally asymptotically stable. The globally stability results are proved using Lyapunov method and LaSalle's invariance principle [9]. Further, this model is extended to an optimal control problem by introducing two types of controls. First control aims to reduce the interaction between susceptibles and infections while the second one aims to provide timely hospitalization for critically ill infections. Our main aim is to reduce the transmission rate of this disease which will lead to the reduction in the number of infections. The optimal control problem is analyzed using Pontryagin's Maximum Principle and is solved numerically using MATLAB. The effectiveness of optimal control is demonstrated by comparing the levels of infected populations with and without optimal control. It has been found that the optimal control strategy gives better result as it reduces the number of infections significantly in the desired period of control. Additionally, it is observed that the optimal control profiles of the control parameters are very much dependent on the cost associated with implementation of these controls. When the weight constants associated with these control parameters increase, optimal control decreases leading to the increase in the number of influenza infections. Finally, numerical simulation is performed to demonstrate the analytical findings.
About the journal
JournalWorld Journal of Modelling and Simulation
PublisherWorld Academic Union
ISSN17467233