Khan Tahir, Zaman Gul, Chohan M Ikhlaq
a Department of Mathematics , University of Malakand, Chakdara Dir (Lower) Khyber Pakhtunkhawa , Pakistan.
b Department of Business Administration and Accounting , Buraimi University College , Al-Buraimi , Oman.
J Biol Dyn. 2017 Dec;11(1):172-189. doi: 10.1080/17513758.2016.1256441.
In this article, we present the transmission dynamic of the acute and chronic hepatitis B epidemic problem and develop an optimal control strategy to control the spread of hepatitis B in a community. In order to do this, first we present the model formulation and find the basic reproduction number [Formula: see text]. We show that if [Formula: see text] then the disease-free equilibrium is both locally as well as globally asymptotically stable. Then, we prove that the model is locally and globally asymptotically stable, if [Formula: see text]. To control the spread of this infection, we develop a control strategy by applying three control variables such as isolation of infected and non-infected individuals, treatment and vaccination to minimize the number of acute infected, chronically infected with hepatitis B individuals and maximize the number of susceptible and recovered individuals. Finally, we present numerical simulation to illustrate the feasibility of the control strategy.
在本文中，我们呈现了急慢性乙型肝炎流行问题的传播动态，并制定了一种最优控制策略以控制乙型肝炎在社区中的传播。为此，首先我们给出模型公式并求出基本再生数[公式：见原文]。我们表明，如果[公式：见原文]，那么无病平衡点局部和全局渐近稳定。然后，我们证明如果[公式：见原文]，该模型局部和全局渐近稳定。为了控制这种感染的传播，我们通过应用三个控制变量，即对感染和未感染个体进行隔离、治疗和接种疫苗，来制定一种控制策略，以尽量减少急性感染、慢性感染乙型肝炎个体的数量，并使易感和康复个体的数量最大化。最后，我们给出数值模拟以说明控制策略的可行性。
