An age-structured diffusive model for epidemic modelling: Lie symmetries and exact solutions
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.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Reaction-diffusion equations in mathematical models arising in epidemiology
The review is devoted to analysis of mathematical models used for describing epidemic processes. A main focus is done on the models that are based on partial differential equations (PDEs), especially those that were deve…
EpidemiologySequential epidemic spread between agglomerates of self-propelled agents in one dimension
Motile organisms can form stable agglomerates such as cities or colonies. In the outbreak of a highly contagious disease, the control of large-scale epidemic spread depends on factors like the number and size of agglomer…
Finite symmetries in agent-based epidemic models
We present an algorithm which explores permutation symmetries to describe the time evolution of agent-based epidemic models. The main idea to improve computation times relies on restricting the stochastic process to one …
Epidemic Information Extraction for Event-Based Surveillance using Large Language Models
This paper presents a novel approach to epidemic surveillance, leveraging the power of Artificial Intelligence and Large Language Models (LLMs) for effective interpretation of unstructured big data sources, like the popu…
In-Context LearningExact solutions for diffusive transport on heterogeneous growing domains
From the smallest biological systems to the largest cosmological structures, spatial domains undergo expansion and contraction. Within these growing domains, diffusive transport is a common phenomenon. Mathematical model…
valid