Damian Knopoff

Seasonally Forced SIR Systems Applied to Respiratory Infectious Diseases, Bifurcations, and Chaos

Publisher: Hindawi Limited

Date: 03-03-2022

DOI: 10.1155/2022/3556043

Abstract: Summary. We investigate models to describe respiratory diseases with fast mutating virus pathogens such that after some years the aquired resistance is lost and hosts can be infected with new variants of the pathogen. Such models were initially suggested for respiartory diseases like influenza, showing complex dynamics in reasonable parameter regions when comparing to historic empirical influenza like illness data, e.g., from Ille de France. The seasonal forcing typical for respiratory diseases gives rise to the different rich dynamical scenarios with even small parameter changes. Especially the seasonality of the infection leads for small values already to period doubling bifurcations into chaos, besides additional coexisting attractors. Such models could in the future also play a role in understanding the presently experienced COVID-19 pandemic, under emerging new variants and with only limited vaccine efficacies against newly upcoming variants. From first period doubling bifurcations, we can eventually infer at which close by parameter regions complex dynamics including deterministic chaos can arise.

Spatially Extended SHAR Epidemiological Framework of Infectious Disease Transmission

Publisher: Hindawi Limited

Date: 13-02-2022

DOI: 10.1155/2022/3304532

Abstract: Mathematical models play an important role in epidemiology. The inclusion of a spatial component in epidemiological models is especially important to understand and address many relevant ecological and public health questions, e.g., when wanting to differentiate transmission patterns across geographical regions or when considering spatially heterogeneous intervention measures. However, the introduction of spatial effects can have significant consequences on the observed model dynamics and hence must be carefully analyzed and interpreted. Cellular automata epidemiological models typically rely on simplified computational grids but can provide valuable insight into the spatial dynamics of transmission within a population by suitably accounting for the connections between in iduals in the considered community. In this paper, we describe a stochastic cellular automata disease model based on an extension of the traditional Susceptible-Infected-Recovered (SIR) compartmentalization of the population, namely, the Susceptible-Hospitalized-Asymptomatic-Recovered (SHAR) formulation, in which infected in iduals either present a severe form of the disease, thus requiring hospitalization, or belong to the so-called mild/asymptomatic class. The critical transmission threshold is derived analytically in the nonspatial SHAR formulation, and this generalizes previously obtained theoretical results for the SIR model. We present simulation results discussing the effect of key model parameters and of spatial correlations on model outputs and propose an algorithm for tracking the evolution of infection clusters within the considered population. Focusing on the role of import and criticality on the overall dynamics, we conclude that the current spatial setting increases the critical transmission threshold in comparison to the nonspatial model.

Politecnico Di Torino

Location: Italy

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Intelligent Biodata SL

Location: Spain

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CONICET Cordoba

Location: Argentina

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Centro Vasco De Matemáticas Aplicadas

Location: Spain

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Universidad Tecnologica Nacional

Location: Argentina

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Universidad Nacional Del Nordeste

Location: Argentina

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Universidad Nacional De Cordoba

Location: Argentina

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Universidad De León Escuela De Ingenierías Industrial E Informática

Location: Spain

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