SIR model with local and global infective contacts: A deterministic approach and applications

TL;DR

This paper introduces a deterministic model for an epidemic spreading on a lattice, incorporating both local and global contacts, and validates it against stochastic simulations for diseases like pertussis and rubella.

Contribution

It presents a novel deterministic approach to a lattice-based SIR model with mixed contact types, aligning well with stochastic results.

Findings

Deterministic model agrees with stochastic simulations across various parameters.

Model effectively captures disease dynamics for pertussis and rubella.

Applicable to epidemic modeling with local and global contact structures.

Abstract

An epidemic model with births and deaths is considered on a two dimensional LxL lattice. Each individual can have global infective contacts according to the standard SIR model rules or local infective contacts with its nearest neighbors. We propose a deterministic approach to this model and verified that there is a good agreement with the stochastic simulations for different situations of the disease transmission and parameters corresponding to pertussis and rubella in the prevaccine era.