<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</abstract>

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.

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

Universidad Distrital Francisco José de Caldas

SIDIS Research Group, Departamento de Matemáticas

Dipartimento di Matematica “Giuseppe Peano” Universita’ di Torino

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

In this paper, the main biological aspects of infectious diseases and their mathematical translation for modeling their transmission dynamics are revised. In...

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

Publié en ligne: 15 oct. 2021

Pages: 1 - 26

Reçu: 16 oct. 2020

Accepté: 18 nov. 2020

DOI: https://doi.org/10.2478/amns.2021.1.00012

Mots clés
Epidemiology, Dynamical systems in biology, Fixed points and periodic points of dynamical systems, Stability of solutions, Bifurcations, Lyapunov global stability and functions, Parameters estimation, Simulation, Disease control

© 2021 Deccy Y. Trejos et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

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

Publié en ligne: 15 oct. 2021

Pages: 1 - 26

Reçu: 16 oct. 2020

Accepté: 18 nov. 2020

DOI: https://doi.org/10.2478/amns.2021.1.00012

Mots clésEpidemiology, Dynamical systems in biology, Fixed points and periodic points of dynamical systems, Stability of solutions, Bifurcations, Lyapunov global stability and functions, Parameters estimation, Simulation, Disease control

© 2021 Deccy Y. Trejos et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Mots clés
Epidemiology, Dynamical systems in biology, Fixed points and periodic points of dynamical systems, Stability of solutions, Bifurcations, Lyapunov global stability and functions, Parameters estimation, Simulation, Disease control