Chaotic dynamics in the seasonally forced SIR epidemic model

Barrientos, Pablo G.; Rodríguez, Jesús; Ruiz-Herrera, Alfonso

doi:10.1007/s00285-017-1130-9

Cited by 37 publications

(22 citation statements)

References 29 publications

(56 reference statements)

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“…An optimum design of a vaccination program requires, apart from financial and logistical considerations, subtle results in epidemiology that are currently not available in the literature. This demand has been magnified because of many populations being subject to vaccination behave in a completely unpredictable manner [2,6]. To overcome this challenge, we have analyzed the role of the pulse vaccination in the classical SIR model.…”

Section: Stretching Properties and Conclusion Definementioning

confidence: 99%

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Paradoxical phenomena and chaotic dynamics in epidemic models subject to vaccination

Herrera¹

2020

Communications on Pure &Amp; Applied Analysis

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An alternative to the constant vaccination strategy could be the administration of a large number of doses on "immunization days" with the aim of maintaining the basic reproduction number to be below one. This strategy, known as pulse vaccination, has been successfully applied for the control of many diseases especially in low-income countries. In this paper, we analytically prove (without being computer-aided) the existence of chaotic dynamics in the classical SIR model with pulse vaccination. To the best of our knowledge, this is the first time in which a theoretical proof of chaotic dynamics is given for an epidemic model subject to pulse vaccination. In a realistic public health context, our analysis suggests that the combination of an insufficient vaccination coverage and high birth rates could produce chaotic dynamics and an increment of the number of infectious individuals.

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Section: Stretching Properties and Conclusion Definementioning

confidence: 99%

“…The geometrical construction seems new and could be applied in different biological situations. The reader can consult [2] for different applications of the method of stretching along the paths in epidemiology.…”

Section: Stretching Properties and Conclusion Definementioning

confidence: 99%

Paradoxical phenomena and chaotic dynamics in epidemic models subject to vaccination

Herrera¹

2020

Communications on Pure &Amp; Applied Analysis

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“…Nevertheless, the transmission rate of many childhood infections and seasonal influenza abruptly changes by the host behavior (cycles of human aggregation such as migrations and school holidays). Inspired by the approach adopted in [19], we assume that can be expressed as…”

Section: Introductionmentioning

confidence: 99%

On the Dynamical Complexity of a Seasonally Forced Discrete SIR Epidemic Model with a Constant Vaccination Strategy

et al. 2018

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In this article, we consider the discretized classical Susceptible-Infected-Recovered (SIR) forced epidemic model to investigate the consequences of the introduction of different transmission rates and the effect of a constant vaccination strategy, providing new numerical and topological insights into the complex dynamics of recurrent diseases. Starting with a constant contact (or transmission) rate, the computation of the spectrum of Lyapunov exponents allows us to identify different chaotic regimes. Studying the evolution of the dynamical variables, a family of unimodal-type iterated maps with a striking biological meaning is detected among those dynamical regimes of the densities of the susceptibles. Using the theory of symbolic dynamics, these iterated maps are characterized based on the computation of an important numerical invariant, the topological entropy. The introduction of a degree (or amplitude) of seasonality, ε, is responsible for inducing complexity into the population dynamics. The resulting dynamical behaviors are studied using some of the previous tools for particular values of the strength of the seasonality forcing, ε. Finally, we carry out a study of the discrete SIR epidemic model under a planned constant vaccination strategy. We examine what effect this vaccination regime will have on the periodic and chaotic dynamics originated by seasonally forced epidemics.

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“…Susceptible, infected, recovered and possibly also exposed classes of a given population need to be considered. Many models have been developed for viral infectious diseases such as Influenza and Ebola [9]- [14] and nearly all of them show chaotic dynamics even after vaccination is administrated [15]. The emergence of chaotic behavior can be attributed mostly to predator-prey and competition dynamics [16]- [18] as well as nonlinear interactions between cell populations such as in cancer models [19]- [22] and Parkinson's disease [23], [24].…”

Section: Introductionmentioning

confidence: 99%

FPGA Realizations of Chaotic Epidemic and Disease Models Including Covid-19

et al. 2021

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The spread of epidemics and diseases is known to exhibit chaotic dynamics; a fact confirmed by many developed mathematical models. However, to the best of our knowledge, no attempt to realize any of these chaotic models in analog or digital electronic form has been reported in the literature. In this work, we report on the efficient FPGA implementations of three different virus spreading models and one disease progress model. In particular, the Ebola, Influenza, and COVID-19 virus spreading models in addition to a Cancer disease progress model are first numerically analyzed for parameter sensitivity via bifurcation diagrams. Subsequently and despite the large number of parameters and large number of multiplication (or division) operations, these models are efficiently implemented on FPGA platforms using fixed-point architectures. Detailed FPGA design process, hardware architecture and timing analysis are provided for three of the studied models (Ebola, Influenza, and Cancer) on an Altera Cyclone IV EP4CE115F29C7 FPGA chip. All models are also implemented on a high performance Xilinx Artix-7 XC7A100TCSG324 FPGA for comparison of the needed hardware resources. Experimental results showing real-time control of the chaotic dynamics are presented.

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Chaotic dynamics in the seasonally forced SIR epidemic model

Cited by 37 publications

References 29 publications

Paradoxical phenomena and chaotic dynamics in epidemic models subject to vaccination

Paradoxical phenomena and chaotic dynamics in epidemic models subject to vaccination

On the Dynamical Complexity of a Seasonally Forced Discrete SIR Epidemic Model with a Constant Vaccination Strategy

FPGA Realizations of Chaotic Epidemic and Disease Models Including Covid-19

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