An age-structured diffusive model for epidemic modelling: Lie symmetries and exact solutions

TL;DR

This paper introduces a new age-structured diffusive epidemic model, analyzes its symmetries, and derives exact solutions including traveling waves, aiding in understanding epidemic dynamics.

Contribution

It generalizes existing models, classifies its Lie symmetries, and constructs exact solutions using symmetry methods, including applications to epidemic data analysis.

Findings

Model admits infinite-dimensional Lie algebra of invariance

Exact traveling wave solutions are constructed

Application demonstrated for epidemic infection counts

Abstract

A new age-structured diffusive model for the mathematical modelling of epidemics is suggested. The model can be considered as a generalization of two models suggested earlier for the same purposes. The Lie symmetry classification of the model is derived. It is shown that the model admits an infinite-dimensional Lie algebra of invariance. Using the Lie symmetries, exact solutions, in particular those of the travelling wave types and in terms of special functions, are constructed. An example of application of the correctly-specified exact solution for calculation of total numbers of infected individuals during an epidemic is presented.