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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Sciendo
2021-10-01
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| Series: | Applied Mathematics and Nonlinear Sciences |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/amns.2021.1.00012 |
| _version_ | 1797800868718837760 |
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| author | Trejos Deccy Y. Valverde Jose C. Venturino Ezio |
| author_facet | Trejos Deccy Y. Valverde Jose C. Venturino Ezio |
| author_sort | Trejos Deccy Y. |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-13T04:41:48Z |
| format | Article |
| id | doaj.art-cfe3e3e973ab40e1af64443cdaf60298 |
| institution | Directory Open Access Journal |
| issn | 2444-8656 |
| language | English |
| last_indexed | 2024-03-13T04:41:48Z |
| publishDate | 2021-10-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Applied Mathematics and Nonlinear Sciences |
| spelling | doaj.art-cfe3e3e973ab40e1af64443cdaf602982023-06-19T05:54:31ZengSciendoApplied Mathematics and Nonlinear Sciences2444-86562021-10-017112610.2478/amns.2021.1.00012Dynamics of infectious diseases: A review of the main biological aspects and their mathematical translationTrejos Deccy Y.0Valverde Jose C.1Venturino Ezio2Facultad de Ciencias y Educación, Universidad Distrital Francisco José de Caldas, Bogotá, Colombia. E-mail:dytrejosa@udistrital.edu.coSIDIS Research Group, Departamento de Matemáticas, Universidad de Castilla-La Mancha, Albacete, SpainGNCS Research Group of the INdAM, Dipartimento di Matematica “Giuseppe Peano” Universita’ di Torino, Torino, ItalyIn 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.https://doi.org/10.2478/amns.2021.1.00012epidemiologydynamical systems in biologyfixed points and periodic points of dynamical systemsstability of solutionsbifurcationslyapunov global stability and functionsparameters estimationsimulationdisease control92d3037n2537c2537c7539a3093d05 |
| spellingShingle | Trejos Deccy Y. Valverde Jose C. Venturino Ezio Dynamics of infectious diseases: A review of the main biological aspects and their mathematical translation Applied Mathematics and Nonlinear Sciences 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 92d30 37n25 37c25 37c75 39a30 93d05 |
| title | Dynamics of infectious diseases: A review of the main biological aspects and their mathematical translation |
| title_full | Dynamics of infectious diseases: A review of the main biological aspects and their mathematical translation |
| title_fullStr | Dynamics of infectious diseases: A review of the main biological aspects and their mathematical translation |
| title_full_unstemmed | Dynamics of infectious diseases: A review of the main biological aspects and their mathematical translation |
| title_short | Dynamics of infectious diseases: A review of the main biological aspects and their mathematical translation |
| title_sort | dynamics of infectious diseases a review of the main biological aspects and their mathematical translation |
| topic | 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 92d30 37n25 37c25 37c75 39a30 93d05 |
| url | https://doi.org/10.2478/amns.2021.1.00012 |
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