Одељење за математику, 23. април 2021.

Наредни састанак Семинара биће одржан онлајн у петак, 23. априла 2021. са  почетком у 14:15.

Предавач: András József Tóbiás, TU Berlin


Апстракт: We investigate a stochastic population model for the infection dynamics of viruses and their microbial hosts when the latter are able to enter with positive probability into a dormant state upon contact with virus particles, thus evading infection. Our work extends the ODE-based approach of Gulbudak and Weitz (2016) to the stochastic individual based scenario, thus taking into account stochastic fluctuations in host- and virus population when their frequencies are low, and also explicitly incorporate a virus reproduction mechanism so that the long-term behaviour of the system can be investigated.

In our analysis, we identify the probability and time of invasion of the epidemic. We show that a positive probability of survival (persistence) of the epidemic is equivalent to the existence of a coexistence equilibrium for the underlying dynamical system. In certain cases, this system exhibits a Hopf bifurcation: If the amount of viruses produced by a single infected cell is high enough, the coexistence equilibrium loses its stability, and numerical results suggest that the system converges to a periodic solution. This is a variant of the „paradox of enrichment“ phenomenon observed in predator-prey type Lotka-Volterra systems. However, for an infection with a sufficiently low mortality rate, such a bifurcation does not occur.

An important finding is that the presence of contact-mediated dormancy somewhat paradoxically enables the host population to maintain high equilibrium sizes (resp. fitness) while still being able to exclude a persistent infection, which is not possible in similar systems without dormancy, where high fitness correlates with high risk of the emergence of a persistent infection. The subject of this talk is joint work with J.Blath.

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