A Mathematical model of the spread of two viral sub-types on a Plant Leaf (Numerical Simulation)

Abstract

Whilst in humans free virus particles and host cells are assumed to be homogenously mixed, in plants, the spatial component is a key factor. The natural proliferation of the virus through a plant is known to happen from a cell to an adjoining cell. When several strains of a virus are present on a plant leaf, the co-infection of a cell by two sub-types is extremely rare. The mechanism which prevents this co-infection is not known in detail. A mathematical model is constructed by modifying the typical Fisher-Kolmogorov equation to understand this mechanism. Two equations are considered, one for each strain. They include the supression of the competitor's type by modifying the reproduction terms in the Fisher-Kolmogorov equations. The hypothesis of co-infection of cells by two viral strains on a plant leaf being extremely rare is tested for the mathematical model presented in this paper. Running simulations of the model shows that this hypothesis is only verified in the symmetric case of the considered rectangular 2-dimensional domain. This means that this model only verifies the hypothesis for the case where both strains are taken at corners of the rectangular domain and when both strains assume equal coefficients. For any biologically realistic case, this mathematical model does not show positive results and is not able to verify the hypothesis.