Dynamics of infectious diseases: A review of the main biological aspects and their mathematical translation

In this paper, the main biological aspects of infectious diseases and their mathematical translation for modeling their transmission dynamics are revised. In particular, some heterogeneity factors which could influence the fitting of the model to reality are pointed out. Mathematical tools and metho...

Full description

Saved in:
Bibliographic Details
Published inApplied mathematics and nonlinear sciences Vol. 7; no. 1; pp. 1 - 26
Main Authors Trejos, Deccy Y., Valverde, Jose C., Venturino, Ezio
Format Journal Article
LanguageEnglish
Published Beirut Sciendo 01.01.2022
De Gruyter Poland
Subjects
37C25
37C75
37N25
39A30
92D30
93D05
Bifurcations
Disease control
Dynamical systems in biology
Epidemiology
Fixed points and periodic points of dynamical systems
Lyapunov global stability and functions
Parameters estimation
Simulation
Stability of solutions
Online AccessGet full text

Cover

More Information
Summary:In this paper, the main biological aspects of infectious diseases and their mathematical translation for modeling their transmission dynamics are revised. In particular, some heterogeneity factors which could influence the fitting of the model to reality are pointed out. Mathematical tools and methods needed to qualitatively analyze deterministic continuous-time models, formulated by ordinary differential equations, are also introduced, while its discrete-time counterparts are properly referenced. In addition, some simulation techniques to validate a mathematical model and to estimate the model parameters are shown. Finally, we present some control strategies usually considered to prevent epidemic outbreaks and their implementation in the model.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:2444-8656
2444-8656
DOI:10.2478/amns.2021.1.00012