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Journals
Applied Mathematics and Nonlinear Sciences
Volume 7 (2022): Issue 1 (January 2022)
Open Access
Dynamics of infectious diseases: A review of the main biological aspects and their mathematical translation
Deccy Y. Trejos
Deccy Y. Trejos
,
Jose C. Valverde
Jose C. Valverde
and
Ezio Venturino
Ezio Venturino
| Oct 15, 2021
Applied Mathematics and Nonlinear Sciences
Volume 7 (2022): Issue 1 (January 2022)
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Published Online:
Oct 15, 2021
Page range:
1 - 26
Received:
Oct 16, 2020
Accepted:
Nov 18, 2020
DOI:
https://doi.org/10.2478/amns.2021.1.00012
Keywords
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.
Fig. 1
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.
Fig. 3
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].
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.
Fig. 6
Bifurcation diagram.
Fig. 7
Transfer diagram for the Ebola compartment model including education as a preventive measure [87].