We introduce non-Markovian SIR epidemic spreading model inspired by the characteristics of the COVID-19, by considering discrete- and continuous-time versions. The distributions of infection intensity and recovery period may take an arbitrary form. By taking corresponding choice of these functions, it is shown that the model reduces to the classical Markovian case. The epidemic threshold is analytically determined for arbitrary functions of infectivity and recovery and verified numerically. The relevance of the model is shown by modeling the first wave of the epidemic in Italy, Spain and the UK, in the spring, 2020.
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http://dx.doi.org/10.1016/j.chaos.2022.112286 | DOI Listing |
Chaos
September 2023
Department of Mathematics, Technical University of Munich, 85748 Garching bei München, Germany.
Self-adaptive dynamics occurs in many fields of research, such as socio-economics, neuroscience, or biophysics. We consider a self-adaptive modeling approach, where adaptation takes place within a set of strategies based on the history of the state of the system. This leads to piecewise deterministic Markovian dynamics coupled to a non-Markovian adaptive mechanism.
View Article and Find Full Text PDFAppl Math Optim
March 2023
Aix-Marseille Univ, CNRS, I2M, Marseille, France.
We study epidemic models where the infectivity of each individual is a random function of the infection age (the elapsed time since infection). To describe the epidemic evolution dynamics, we use a stochastic process that tracks the number of individuals at each time that have been infected for less than or equal to a certain amount of time, together with the aggregate infectivity process. We establish the functional law of large numbers (FLLN) for the stochastic processes that describe the epidemic dynamics.
View Article and Find Full Text PDFMath Biosci Eng
January 2023
Mathematical Biosciences Institute and the Division of Biostatistics, College of Public Health, The Ohio State University, Cunz Hall, 1841 Neil Avenue, Columbus, OH 43210, USA.
The Dynamical Survival Analysis (DSA) is a framework for modeling epidemics based on mean field dynamics applied to individual (agent) level history of infection and recovery. Recently, the Dynamical Survival Analysis (DSA) method has been shown to be an effective tool in analyzing complex non-Markovian epidemic processes that are otherwise difficult to handle using standard methods. One of the advantages of Dynamical Survival Analysis (DSA) is its representation of typical epidemic data in a simple although not explicit form that involves solutions of certain differential equations.
View Article and Find Full Text PDFChaos Solitons Fractals
July 2022
SS. Cyril and Methodius University, Faculty of Computer Science and Engineering, Rudzer Boshkovikj 16, P.O. Box 393, 1000 Skopje, Macedonia.
We introduce non-Markovian SIR epidemic spreading model inspired by the characteristics of the COVID-19, by considering discrete- and continuous-time versions. The distributions of infection intensity and recovery period may take an arbitrary form. By taking corresponding choice of these functions, it is shown that the model reduces to the classical Markovian case.
View Article and Find Full Text PDFSci Rep
March 2022
Faculty of Engineering Sciences, Kyushu University, Kasuga-koen, Kasuga-shi, Fukuoka, 816-8580, Japan.
We present the pair approximation models for susceptible-infected-recovered (SIR) epidemic dynamics in a sparse network based on a regular network. Two processes are considered, namely, a Markovian process with a constant recovery rate and a non-Markovian process with a fixed recovery time. We derive the implicit analytical expression for the final epidemic size and explicitly show the epidemic threshold in both Markovian and non-Markovian processes.
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