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Advisor(s)
Abstract(s)
Despite numerous studies of epidemiological systems, the role of seasonality in the
recurrent epidemics is not entirely understood. During certain periods of the year
incidence rates of a number of endemic infectious diseases may fluctuate dramatically.
This influences the dynamics of mathematical models describing the spread
of infection and often leads to chaotic oscillations. In this paper, we are concerned
with a generalization of a classical Susceptible–Infected–Recovered epidemic model
which accounts for seasonal effects. Combining numerical and analytic techniques,
we gain new insights into the complex dynamics of a recurrent disease influenced by
the seasonality. Computation of the Lyapunov spectrum allows us to identify different
chaotic regimes, determine the fractal dimension and estimate the predictability of the
appearance of attractors in the system. Applying the homotopy analysis method, we
obtain series solutions to the original nonautonomous SIR model with a high level of
accuracy and use these approximations to analyze the dynamics of the system. The
efficiency of the method is guaranteed by the optimal choice of an auxiliary control
parameter which ensures the rapid convergence of the series to the exact solution of
the forced SIR epidemic model.
Description
Keywords
Explicit solutions SIR epidemic model Seasonal fluctuations Chaotic behavior Flutuações sazonais Comportamento caótico
Citation
DUARTE, Jorge; [et al] – Chaos analysis and explicit series solutions to the seasonally forced SIR epidemic model. Journal of Mathematical Biology. ISSN 1432-1416. Vol. 78, N.º 7 (2019), pp. 2235-2258
Publisher
Springer Verlag