Endemic state equivalence between non-Markovian SEIS and Markovian SIS model in complex networks
Journal
Physica A: Statistical Mechanics and its Applications
Date Issued
2022-08-01
Author(s)
Tomovski, Igor
Abazi, Alajdin
Abstract
In the light of several major epidemic events that emerged in the past two
decades, and emphasized by the COVID-19 pandemics, the non-Markovian spreading
models occurring on complex networks gained significant attention from the scientific
community. Following this interest, in this article, we explore the relations that exist
between the non-Markovian SEIS (Susceptible–Exposed–Infectious–Susceptible) and
the classical Markov SIS, as basic re-occurring virus spreading models in complex
networks. We investigate the similarities and seek for equivalences both for the discretetime and the continuous-time forms. First, we formally introduce the continuous-time
non-Markovian SEIS model, and derive the epidemic threshold in a strict mathematical
procedure. Then we present the main result of the paper that, providing certain
relations between process parameters hold, the stationary-state solutions of the status
probabilities in the non-Markovian SEIS may be found from the stationary state
probabilities of the Markov SIS model. This result has a two-fold significance.
First, it simplifies the computational complexity of the non-Markovian model in
practical applications, where only the stationary distribution of the state probabilities
is required. Next, it defines the epidemic threshold of the non-Markovian SEIS model,
without the necessity of a thrall mathematical analysis. We present this result both
in analytical form, and confirm the result trough numerical simulations. Furthermore,
as of secondary importance, in an analytical procedure we show that each Markov SIS
may be represented as non-Markovian SEIS model.
decades, and emphasized by the COVID-19 pandemics, the non-Markovian spreading
models occurring on complex networks gained significant attention from the scientific
community. Following this interest, in this article, we explore the relations that exist
between the non-Markovian SEIS (Susceptible–Exposed–Infectious–Susceptible) and
the classical Markov SIS, as basic re-occurring virus spreading models in complex
networks. We investigate the similarities and seek for equivalences both for the discretetime and the continuous-time forms. First, we formally introduce the continuous-time
non-Markovian SEIS model, and derive the epidemic threshold in a strict mathematical
procedure. Then we present the main result of the paper that, providing certain
relations between process parameters hold, the stationary-state solutions of the status
probabilities in the non-Markovian SEIS may be found from the stationary state
probabilities of the Markov SIS model. This result has a two-fold significance.
First, it simplifies the computational complexity of the non-Markovian model in
practical applications, where only the stationary distribution of the state probabilities
is required. Next, it defines the epidemic threshold of the non-Markovian SEIS model,
without the necessity of a thrall mathematical analysis. We present this result both
in analytical form, and confirm the result trough numerical simulations. Furthermore,
as of secondary importance, in an analytical procedure we show that each Markov SIS
may be represented as non-Markovian SEIS model.
Subjects
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