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Control, bi-stability, and preference for chaos in time-dependent vaccination campaign

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Autor(es):
Gabrick, Enrique C. ; Brugnago, Eduardo L. ; de Moraes, Ana L. R. ; Protachevicz, Paulo R. ; da Silva, Sidney T. ; Borges, Fernando S. ; Caldas, Ibere L. ; Batista, Antonio M. ; Kurths, Juergen
Número total de Autores: 9
Tipo de documento: Artigo Científico
Fonte: Chaos; v. 34, n. 9, p. 13-pg., 2024-09-01.
Resumo

In this work, effects of constant and time-dependent vaccination rates on the Susceptible-Exposed-Infected-Recovered-Susceptible (SEIRS) seasonal model are studied. Computing the Lyapunov exponent, we show that typical complex structures, such as shrimps, emerge for given combinations of a constant vaccination rate and another model parameter. In some specific cases, the constant vaccination does not act as a chaotic suppressor and chaotic bands can exist for high levels of vaccination (e.g., > 0.95). Moreover, we obtain linear and non-linear relationships between one control parameter and constant vaccination to establish a disease-free solution. We also verify that the total infected number does not change whether the dynamics is chaotic or periodic. The introduction of a time-dependent vaccine is made by the inclusion of a periodic function with a defined amplitude and frequency. For this case, we investigate the effects of different amplitudes and frequencies on chaotic attractors, yielding low, medium, and high seasonality degrees of contacts. Depending on the parameters of the time-dependent vaccination function, chaotic structures can be controlled and become periodic structures. For a given set of parameters, these structures are accessed mostly via crisis and, in some cases, via period-doubling. After that, we investigate how the time-dependent vaccine acts in bi-stable dynamics when chaotic and periodic attractors coexist. We identify that this kind of vaccination acts as a control by destroying almost all the periodic basins. We explain this by the fact that chaotic attractors exhibit more desirable characteristics for epidemics than periodic ones in a bi-stable state. (AU)

Processo FAPESP: 20/04624-2 - Plasticidade sináptica em redes neuronais
Beneficiário:Paulo Ricardo Protachevicz
Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
Processo FAPESP: 18/03211-6 - Dinâmica não linear
Beneficiário:Iberê Luiz Caldas
Modalidade de apoio: Auxílio à Pesquisa - Temático
Processo FAPESP: 23/12863-5 - Sincronização em redes neuronais com plasticidade sináptica de longa duração
Beneficiário:Paulo Ricardo Protachevicz
Modalidade de apoio: Bolsas no Exterior - Estágio de Pesquisa - Pós-Doutorado
Processo FAPESP: 21/12232-0 - Transporte caótico de partículas
Beneficiário:Eduardo Luís Brugnago
Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
Processo FAPESP: 22/13761-9 - Dinâmica de Sistemas Complexos
Beneficiário:Iberê Luiz Caldas
Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Brasil