• Underwhelming the immune response: Effect of slow virus growth on CD8+-T-lymphocyte responses

      Bocharov, Gennady; Burkhard, Ludewig; Bertoletti, Antonio; Klenerman, Paul; Junt, Tobias; Krebs, Philippe; Luzyanina, Tatyana; Fraser, Cristophe; Anderson, Roy M.; University of London/Institute of Numerical Mathematics, Russian Academy of Sciences ; University of Zurich ; University College London ; Oxford University ; University of Zurich ; University of Zurich ; Leuven University ; University of London ; University of London (American Society for Microbiology, 2004-02-12)
      The speed of virus replication has typically been seen as an advantage for a virus in overcoming the ability of the immune system to control its population growth. Under some circumstances, the converse may also be true: more slowly replicating viruses may evoke weaker cellular immune responses and therefore enhance their likelihood of persistence. Using the model of lymphocytic choriomeningitis virus (LCMV) infection in mice, we provide evidence that slowly replicating strains induce weaker cytotoxic-T-lymphocyte (CTL) responses than a more rapidly replicating strain. Conceptually, we show a "bell-shaped" relationship between the LCMV growth rate and the peak CTL response. Quantitative analysis of human hepatitis C virus infections suggests that a reduction in virus growth rate between patients during the incubation period is associated with a spectrum of disease outcomes, from fulminant hepatitis at the highest rate of viral replication through acute resolving to chronic persistence at the lowest rate. A mathematical model for virus-CTL population dynamics (analogous to predator [CTL]-prey [virus] interactions) is applied in the clinical data-driven analysis of acute hepatitis B virus infection. The speed of viral replication, through its stimulus of host CTL responses, represents an important factor influencing the pathogenesis and duration of virus persistence within the human host. Viruses with lower growth rates may persist in the host because they "sneak through" immune surveillance.
    • Units of the group algebra of the group $C_n\times D_6$ over any finite field of characteristic $3$

      Gildea, Joe; Taylor, Rhian; University of Chester (International Electronic Journal of Algebra, 2018-07-05)
      In this paper, we establish the structure of the unit group of the group algebra ${\FF}_{3^t}(C_n\times D_6)$ for $n \geq 1$.
    • Using approximations to Lyapunov exponents to predict changes in dynamical behaviour in numerical solutions to stochastic delay differential equations

      Ford, Neville J.; Norton, Stewart J.; University of Chester (Springer, 2006-10-30)
      This book chapter explores the parameter values at which there are changes in qualitative behaviour of the numerical solutions to parameter-dependent linear stochastic delay differential equations with multiplicative noise. A possible tool in this analysis is the calculation of the approximate local Lyapunov exponents. We show that estimates for the maximal local Lyapunov exponent have predictable distributions dependent upon the parameter values and the fixed step length of the numerical method, and that changes in the qualitative behaviour of the solutions occur at parameter values that depend on the step length.
    • Volterra integral equations and fractional calculus: Do neighbouring solutions intersect?

      Diethelm, Kai; Ford, Neville J.; Technische Universität Braunschweig ; University of Chester (Rocky Mountain Mathematics Consortium, 2012-04-04)
      This journal article considers the question of whether or not the solutions to two Volterra integral equations which have the same kernel but different forcing terms may intersect at some future time.