A measure-valued stochastic model for vector-borne viruses

TL;DR

This paper introduces a measure-valued stochastic model for vector-borne viruses that captures phenotypic and spatial dynamics, and derives macroscopic integro-differential equations to describe large-scale behavior.

Contribution

It presents a novel measure-valued stochastic framework for vector-borne viruses and derives macroscopic integro-differential equations from microscopic models.

Findings

Model can infer virus extinction probabilities.

Derivation of integro-differential equations as large-scale limits.

Propagation of initial density properties over time.

Abstract

In this work we propose a measure-valued stochastic process representing the dynamics of a virus population, structured by phenotypic traits and geographical space, and where viruses are transported between spatial locations by mechanical vectors. As a first example of the use of this model, we show how to use this model to infer results on the probability of extinction of the virus population. Later, by combining various scalings on population sizes, speed of diffusion of vectors, and other relevant model parameters, we show the emergence of two systems of integro-differential equations as Macroscopic descriptions of the system. Under the existence of densities at time zero, we also show the propagation of this property for later times, and derive the strong formulation of the limiting systems of IDEs. These strong formulations, in a sense, correspond to spatial Lotka-Volterra competition models with mutation and vector-borne dispersal.