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

Deccy Y. Trejos

Deccy Y. Trejos

Facultad de Ciencias y Educación, Universidad Distrital Francisco José de CaldasBogotá, Colombia
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Trejos, Deccy Y.
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Jose C. Valverde

Jose C. Valverde

SIDIS Research Group, Departamento de Matemáticas, Universidad de Castilla-La ManchaAlbacete, Spain
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Valverde, Jose C.
 und 
Ezio Venturino

Ezio Venturino

GNCS Research Group of the INdAM, Dipartimento di Matematica “Giuseppe Peano” Universita’ di TorinoTorino, Italy
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Venturino, Ezio
  
15. Okt. 2021
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Online veröffentlicht: 15. Okt. 2021
Seitenbereich: 1 - 26
Eingereicht: 16. Okt. 2020
Akzeptiert: 18. Nov. 2020
DOI: https://doi.org/10.2478/amns.2021.1.00012
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© 2021 Deccy Y. Trejos et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

Transfer diagram for an SIR compartment model
Transfer diagram for an SIR compartment model

Fig. 2

Diagram for the mathematical model for the dynamics of the zika virus in human and mosquito populations.
Diagram for the mathematical model for the dynamics of the zika virus in human and mosquito populations.

Fig. 3

Transfer diagram for an SIR metapopulation compartmental model (see [91]).
Transfer diagram for an SIR metapopulation compartmental model (see [91]).

Fig. 4

Homogeneous compartmental model versus heterogeneous contact model. For the compartment model the disease spreads along the arrows (left figure) and in the net model the disease spreads through the edges (right figure) [94].
Homogeneous compartmental model versus heterogeneous contact model. For the compartment model the disease spreads along the arrows (left figure) and in the net model the disease spreads through the edges (right figure) [94].

Fig. 5

An example of an SIR model structured by age groups. The population is partitioned into two age groups, juvenile, and adult, and in each of these age groups the subpopulation is again partitioned into susceptible (S), infected (I) and recovered (R). Each of these age groups has a different level of interaction within their own age group and with people from the other groups.
An example of an SIR model structured by age groups. The population is partitioned into two age groups, juvenile, and adult, and in each of these age groups the subpopulation is again partitioned into susceptible (S), infected (I) and recovered (R). Each of these age groups has a different level of interaction within their own age group and with people from the other groups.

Fig. 6

Bifurcation diagram.
Bifurcation diagram.

Fig. 7

Transfer diagram for the Ebola compartment model including education as a preventive measure [87].
Transfer diagram for the Ebola compartment model including education as a preventive measure [87].
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Biologie, Biologie, andere, Mathematik, Angewandte Mathematik, Mathematik, Allgemeines, Physik, Physik, andere
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