The persistence of a local dialect when a national standard language is present - a mathematical model

Koichi Saeki

2016/11/07, 13:30 - , at W1-C-909

There are two types of viral infections in a host, one is global and the other is local. Global infection means that an infected cell produce viral particles that travel to susceptible cells somewhere. In contrast, local infection occurs via physical contact between an infected cell and a susceptible cell. The emergence of mutant virus that has a high ability of local infection is observed in vitro and suggested in vivo, and those mutants are considered to have a relationship with a severe disease caused by virus infection.
     Here we attempt to reveal what is the evolutionarily stable proportion of global and local infection, and how it depends on the spatial parameters. We consider a lattice space in which each site is occupied by either a target or a non-target cell for virus, and assume that whether a site is occupied by a target cell or a non-target cell will never change. Then, how target and non-target cells are distributed over the lattice space is parameterized by the frequency of target cells and the pair frequency of target cells.
     At first, the infection dynamics are modeled by pair approximation and the endemic condition for a virus with a certain proportion of global infection is calculated. Next, the evolutionarily stable strategy is obtained by an invasibility analysis using pair approximated dynamics. The results show that higher proportion of local infection is selected as target cells become clustered. We also observe the parameter region that even if global infection is more efficient than local one, using local infection at a certain rate becomes the optimal due to spatial clustering of target cells.

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