By Dominik Wodarz

This e-book studies how mathematical and computational techniques could be valuable to aid us know how killer T-cell responses paintings to struggle viral infections. It additionally demonstrates, in a writing sort that exemplifies the purpose, that such mathematical and computational techniques are most beneficial while coupled with experimental paintings via interdisciplinary collaborations. Designed to be worthy to immunoligists and viroligists with no vast computational historical past, the publication covers a wide number of themes, together with either uncomplicated immunological questions and the appliance of those insights to the certainty and remedy of pathogenic human illnesses.

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**Extra info for Killer Cell Dynamics: Mathematical and Computational Approaches to Immunology **

**Example text**

Mathematical models suggest that a combination of three drugs should be used [Ribeiro et al. (1998)]. If a single drug is used, it is very likely that at least one resistant mutant exists upon initiation of treatment. If two drugs are used, this likelihood is lowered but still relatively large. 5 Virus Dynamics and Mathematical Modeling 21 if three drugs are used in combination, then it is extremely unlikely that a mutant that is resistant against all drugs in use is found upon start of therapy.

We assume that eﬀector CTL are simply proportional to the number of memory CTL and the amount of antigen (expressed by the term cqyw). That is, we make a quasi steady state assumption. Assume that the the basic reproductive ratio of the virus is greater than one. A sustained immune response can become established if c(1 − q)(λ/a − d/β) > b. In this case, the system converges to the following equilibrium. λc(1 − q) , dc(1 − q) + bβ b y∗ = , c(1 − q) z ∗ h(1 − q) , w∗ = bq βx∗ − a z∗ = . 17) According to these expressions, virus load is reduced by a high responsiveness and a long life span of the memory CTLp.

In this case, CTL divisions are independent of antigenic stimulation. This provides an initial disadvantage: as virus load grows, the increased level of antigenic stimulation does not result in faster CTL expansion and the virus can more easily grow to high levels and cause acute pathology. As virus load is reduced to low levels by the CTL, however, the CTL can keep dividing despite the small amounts of antigenic stimulation. Thus, in contrast to the continuous stimulation model, production of eﬀectors does not slow down abruptly as virus load drops.