A hybrid SIRS+V model of infection spread

Abstract

We build a model of the infection spread in the form of a system
of differential equations that takes into account the inertial nature of the transfer
of infection between individuals.
A modified SIRS model
of epidemic spread is constructed in the form of a system of ordinary differential equations of the third
order. It differs from standard models by considering the inertial
nature of the infection transmission process between individuals of the population, which
is realized by introducing a "carrier agent" into the model.
The model does not take into account the influence of the disease on the population size,
while population density is regarded as a parameter influencing
the course of the epidemic. The dynamics of the model shows a good qualitative
correspondence with a variety of phenomena observed in the evolution of diseases.
The suggested complication of the standard SIRS model by
adding to it an equation for the dynamics of the pathogen of infection presents
prospects for its specification via more precise adjustment to
specific diseases, as well as taking into account the heterogeneity in the distribution
of individuals and the pathogen in space. Further modification of the model can go through complicating the function which defines the probability of infection, generation and inactivation of the pathogen, the influence of climatic factors, as well as by means of transition to spatially distributed
systems, for example, networks of probabilistic cellular automata.

Speaker

Alexey Shabunin
Saratov State University
Russia

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