title: The transmission dynamic and optimal control of acute and chronic hepatitis B.
abstract: 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.
authors.affiliation: a Department of Mathematics , University of Malakand, Chakdara Dir (Lower) Khyber Pakhtunkhawa , Pakistan.
authors.forename: Tahir
authors.initials: T
authors.lastname: Khan
authors.affiliation: a Department of Mathematics , University of Malakand, Chakdara Dir (Lower) Khyber Pakhtunkhawa , Pakistan.
authors.forename: Gul
authors.initials: G
authors.lastname: Zaman
authors.affiliation: b Department of Business Administration and Accounting , Buraimi University College , Al-Buraimi , Oman.
authors.forename: M Ikhlaq
authors.initials: MI
authors.lastname: Chohan
mesh_terms: D050936:Basic Reproduction Number; D058872:Epidemics; D019694:Hepatitis B, Chronic / Q000517:prevention & control* / Q000635:transmission*; D006801:Humans; D008954:Models, Biological
keywords: 49J15; 92D25; 93D20; Epidemic model; basic reproduction number; numerical simulation; optimal control strategy; stability analysis