Dissertação
Modelos epidemiológicos em tempo discreto
Fecha
2022-08-25Autor
Morin, Luiza Santos
Institución
Resumen
In an endemics, an infeccious disease remains prevalent, in low levels, in a population. In this
work, three discrete time mathematical models for an endemic disease are studied: the SIR,
the SEIR and SEIRS models. For the qualitative analysis of the models, Discrete Dynamical
Systems techniques are used, through which the equilibrium solutions and their stability and the
Basic Reproductive Number of each model are determined. In addition, the results are illustrated through numerical simulations. A careful comparison of the properties of the models reveals
that they all exhibit damped oscillations as the number of susceptible, infectious, and recovered
approaches the endemic equilibrium. In the SEIR model, the latency period slows down the
spread of infection compared to the SIR model. When there is loss of immunity (SEIRS model)
the levels of infectious are higher.