title: Spatiotemporal Dynamics of Virus Infection Spreading in Tissues.
abstract: Virus spreading in tissues is determined by virus transport, virus multiplication in host cells and the virus-induced immune response. Cytotoxic T cells remove infected cells with a rate determined by the infection level. The intensity of the immune response has a bell-shaped dependence on the concentration of virus, i.e., it increases at low and decays at high infection levels. A combination of these effects and a time delay in the immune response determine the development of virus infection in tissues like spleen or lymph nodes. The mathematical model described in this work consists of reaction-diffusion equations with a delay. It shows that the different regimes of infection spreading like the establishment of a low level infection, a high level infection or a transition between both are determined by the initial virus load and by the intensity of the immune response. The dynamics of the model solutions include simple and composed waves, and periodic and aperiodic oscillations. The results of analytical and numerical studies of the model provide a systematic basis for a quantitative understanding and interpretation of the determinants of the infection process in target organs and tissues from the image-derived data as well as of the spatiotemporal mechanisms of viral disease pathogenesis, and have direct implications for a biopsy-based medical testing of the chronic infection processes caused by viruses, e.g. HIV, HCV and HBV.
authors.affiliation: Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, Russian Federation.|Gamaleya Center of Epidemiology and Microbiology, Moscow, Russian Federation.|RUDN University, Moscow, Russian Federation.
authors.forename: Gennady
authors.identifier: http://orcid.org/0000-0002-5049-0656
authors.initials: G
authors.lastname: Bocharov
authors.affiliation: Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, Russian Federation.|Infection Biology Laboratory, Department of Experimental and Health Sciences, Universitat Pompeu Fabra, Barcelona, Spain.|ICREA, Pg. Lluís Companys 23, Barcelona, Spain.
authors.forename: Andreas
authors.initials: A
authors.lastname: Meyerhans
authors.affiliation: Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, Saint Petersburg, Russian Federation.
authors.forename: Nickolai
authors.initials: N
authors.lastname: Bessonov
authors.affiliation: Instituto de Matemática y Fisica, Universidad de Talca, Talca, Chile.
authors.forename: Sergei
authors.initials: S
authors.lastname: Trofimchuk
authors.affiliation: Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, Russian Federation.|Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, Villeurbanne, France.|INRIA Team Dracula, INRIA Lyon La Doua, Villeurbanne, France.|Laboratoire Poncelet, UMI 2615 CNRS, Moscow, Russian Federation.
authors.forename: Vitaly
authors.initials: V
authors.lastname: Volpert
mesh_terms: D015658:HIV Infections / Q000276:immunology*; D015497:HIV-1 / Q000276:immunology*; D016174:Hepacivirus / Q000276:immunology*; D006509:Hepatitis B / Q000276:immunology*; D006515:Hepatitis B virus / Q000276:immunology*; D006526:Hepatitis C / Q000276:immunology*; D006801:Humans; D018448:Models, Immunological