title: Mathematical modeling of transmission dynamics and optimal control of vaccination and treatment for hepatitis B virus.
abstract: Hepatitis B virus (HBV) infection is a worldwide public health problem. In this paper, we study the dynamics of hepatitis B virus (HBV) infection which can be controlled by vaccination as well as treatment. Initially we consider constant controls for both vaccination and treatment. In the constant controls case, by determining the basic reproduction number, we study the existence and stability of the disease-free and endemic steady-state solutions of the model. Next, we take the controls as time and formulate the appropriate optimal control problem and obtain the optimal control strategy to minimize both the number of infectious humans and the associated costs. Finally at the end numerical simulation results show that optimal combination of vaccination and treatment is the most effective way to control hepatitis B virus infection.
authors.affiliation: Department of Mathematics Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.
authors.forename: Ali Vahidian
authors.initials: AV
authors.lastname: Kamyad
authors.affiliation: Department of Mathematical Sciences, Payame Noor University, Iran.
authors.forename: Reza
authors.identifier: 0000-0002-2972-4091
authors.initials: R
authors.lastname: Akbari
authors.affiliation: Research Center for Infection Control and Hand Hygiene, Mashhad University of Medical Sciences, Mashhad, Iran.
authors.forename: Ali Akbar
authors.initials: AA
authors.lastname: Heydari
authors.affiliation: Payame Noor University, Khorasan Razavi, Mashhad, Iran.
authors.forename: Aghileh
authors.initials: A
authors.lastname: Heydari
mesh_terms: D000324:Adrenocorticotropic Hormone / Q000378:metabolism; D000465:Algorithms; D001424:Bacterial Infections / Q000378:metabolism; D019295:Computational Biology / Q000379:methods; D003346:Corticotropin-Releasing Hormone / Q000378:metabolism; D006509:Hepatitis B / Q000628:therapy*; D006515:Hepatitis B virus; D006801:Humans; D006854:Hydrocortisone / Q000378:metabolism; D007375:Interleukin-1 / Q000378:metabolism; D008264:Macrophages / Q000166:cytology; D008962:Models, Theoretical; D009490:Neurosecretory Systems; D013997:Time Factors; D014611:Vaccination; D014761:Viral Hepatitis Vaccines / Q000627:therapeutic use*
chemical_list: D007375:Interleukin-1; D014761:Viral Hepatitis Vaccines; D000324:Adrenocorticotropic Hormone; D003346:Corticotropin-Releasing Hormone; D006854:Hydrocortisone