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Spatial and stochastic effects in a model of viral infection. (English) Zbl 1306.92057

Summary: Recently, a mathematical model of dynamics of viral infection has been proposed that consists of reaction-diffusion type differential equations for wild-type and infected cells, virions and interferon. The model serves as a mathematical description for two-dimensional viral infection spread experiments. We built a model which is different and is an extension of another model by Ph. Getto et al. [J. Math. Anal. Appl. 344, No. 2, 821–850 (2008; Zbl 1137.92019)]. We investigated its deterministic and stochastic versions, using modeling software sbioPN created by the first author. We found that in the range of parameters, which may be called “critical”, the stochastic model seems to display complex effects qualitatively different from its deterministic counterpart. Also, the rates of infection in the stochastic model are generally slower than in the deterministic model, an effect, which can be traced to Jensen inequality known best in probability calculus. Although a direct experimental confirmation of these effects is still missing, they seem sufficiently interesting to deserve discussion.

MSC:

92D30 Epidemiology

Citations:

Zbl 1137.92019

Software:

sbioPN
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