@misc{Proell2013,
  type      = {Master Thesis},
  author    = {Pr{\"o}ll, Sebastian},
  title     = {Stability of Switched Epidemiological Models},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-108573},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2013},
  abstract  = {In this thesis it is shown how the spread of infectious diseases can be described via mathematical models that show the dynamic behavior of epidemics. Ordinary differential equations are used for the modeling process. SIR and SIRS models are distinguished, depending on whether a disease confers immunity to individuals after recovery or not. There are characteristic parameters for each disease like the infection rate or the recovery rate. These parameters indicate how aggressive a disease acts and how long it takes for an individual to recover, respectively. In general the parameters are time-varying and depend on population groups. For this reason, models with multiple subgroups are introduced, and switched systems are used to carry out time-variant parameters. When investigating such models, the so called disease-free equilibrium is of interest, where no infectives appear within the population. The question is whether there are conditions, under which this equilibrium is stable. Necessary mathematical tools for the stability analysis are presented. The theory of ordinary differential equations, including Lyapunov stability theory, is fundamental. Moreover, convex and nonsmooth analysis, positive systems and differential inclusions are introduced. With these tools, sufficient conditions are given for the disease-free equilibrium of SIS, SIR and SIRS systems to be asymptotically stable.},
  subject      = {Gew{\"o}hnliche Differentialgleichung},
  language  = {en}
}
@book{BockGauchGiernatetal.2013,
  author    = {Bock, Stefanie and Gauch, Fabian and Giernat, Yannik and Hillebrand, Frank and Kozlova, Darja and Linck, Lisa and Moschall, Rebecca and Sauer, Markus and Schenk, Christian and Ulrich, Kristina and Bodem, Jochen},
  title     = {HIV-1 : Lehrbuch von Studenten f{\"u}r Studenten},
  organization    = {Bachelor- und Masterkurs Virologie 2013},
  isbn      = {978-3-923959-90-7},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-78980},
  publisher      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2013},
  abstract  = {Dies ist ein Lehrbuch {\"u}ber die HIV-1 Replikation, Pathogenese und Therapie. Es richtet sich an Studenten der Biologie und der Medizin, die etwas mehr {\"u}ber HIV erfahren wollen und stellt neben virologischen Themen auch die zellul{\"a}ren Grundlagen dar. Es umfasst den Viruseintritt, die reverse Transkription, Genom-Integration, Transkriptionsregualtion, die Kotrolle des Spleißens, der Polyadenylierung und des RNA-Exportes. Die Darstellung wird abgerundet mit Kapiteln zum intrazellul{\"a}rem Transport, zu Nef und zum Virusassembly. In zwei weiteren Kapitel wird die HIV-1 Pathogenese und die Therapie besprochen. Zur Lernkontrolle sind den Kapiteln Fragen und auch Klausurfragen angef{\"u}gt.},
  subject      = {HIV},
  language  = {de}
}