Extended SIR Models with Nonstandard Diffusion: Their Properties and Symmetry Analysis
Date
2024-04-17
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
ORCID
Type
Thesis
Degree Level
Masters
Abstract
SIR (Susceptible-Infected-Recovered)-based models are systems of ordinary differential equations (ODEs). The assumption of population mobility incorporates the diffusion of infected individuals in the incidence rate of the diseases, and transforms the system of ODEs into a system of partial differential equations (PDEs). In this thesis, we focus on the non-standard diffusion SIR PDE model, which describes the spread of infection through a spatially varying population. Additionally, we modify the novel model by considering birth and internal conflict for the susceptible population, implementing logistic growth, and accounting for a constant death rate for all compartments. These adjustments aim to make the model more realistic and illustrate how diseases interact with demographic factors within populations.
In our exploration of the non-standard diffusion SIR model, described by systems of PDEs, we conduct a symmetry classification of the PDE family and derive some reductions to ODEs or ODE systems. We employ a combination of analytical and numerical techniques to compute resulting solutions, which satisfy a simple boundary value problem and model incoming infection waves.
Description
Keywords
SIR models, space-time SIR models with nonstandard diffusion, buffer zone, quasi-periodicity, waves, symmetries, exact solutions
Citation
Degree
Master of Science (M.Sc.)
Department
Mathematics and Statistics
Program
Mathematics