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Journal Article

Impact of periodic vaccination in SEIRS seasonal model


Gabrick,  Enrique C.
Potsdam Institute for Climate Impact Research;

Brugnago,  Eduardo
External Organizations;

de Souza,  Silvio
External Organizations;

Iarosz,  Kelly
External Organizations;

Szeszech,  Jose
External Organizations;

Viana,  Ricardo
External Organizations;

Caldas,  Ibere
External Organizations;

Batista,  Antonio
External Organizations;


Kurths,  Jürgen
Potsdam Institute for Climate Impact Research;

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Gabrick, E. C., Brugnago, E., de Souza, S., Iarosz, K., Szeszech, J., Viana, R., Caldas, I., Batista, A., Kurths, J. (2024): Impact of periodic vaccination in SEIRS seasonal model. - Chaos, 34, 1, 013137.

Cite as: https://publications.pik-potsdam.de/pubman/item/item_29685
We study three different strategies of vaccination in an SEIRS (Susceptible–Exposed–Infected–Recovered–Susceptible) seasonal forced model, which are (⁠ ⁠) continuous vaccination; (⁠ ⁠) periodic short-time localized vaccination, and (⁠ ⁠) periodic pulsed width campaign. Considering the first strategy, we obtain an expression for the basic reproduction number and infer a minimum vaccination rate necessary to ensure the stability of the disease-free equilibrium (DFE) solution. In the second strategy, short duration pulses are added to a constant baseline vaccination rate. The pulse is applied according to the seasonal forcing phases. The best outcome is obtained by locating intensive immunization at inflection of the transmissivity curve. Therefore, a vaccination rate of of susceptible individuals is enough to ensure DFE. For the third vaccination proposal, additionally to the amplitude, the pulses have a prolonged time width. We obtain a non-linear relationship between vaccination rates and the duration of the campaign. Our simulations show that the baseline rates, as well as the pulse duration, can substantially improve the vaccination campaign effectiveness. These findings are in agreement with our analytical expression. We show a relationship between the vaccination parameters and the accumulated number of infected individuals, over the years, and show the relevance of the immunization campaign annual reaching for controlling the infection spreading. Regarding the dynamical behavior of the model, our simulations show that chaotic and periodic solutions as well as bi-stable regions depend on the vaccination parameters range.