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Spatial and Stochastic Effects in a Model of Viral Infection

Bertolusso R., Kimmel M.

Fundamenta Informaticae

2012

Vol. 118, nr 4

327-343

Recently, Haseltine et al. published a mathematical model of dynamics of viral infection that has consisted 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 from Haseltine’s and is an ex- tension of another model by Getto et al. We investigated its deterministic and stochastic versions, using modeling software sbioPN created by Bertolusso. 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.