Global stability in a networked SIR epidemic model

Tian, Canrong; Zhang, Qunying; Zhang, Lai

doi:10.1016/j.aml.2020.106444

Cited by 62 publications

(45 citation statements)

References 8 publications

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“…Many analytical studies assume this simplification (e.g., [21,20,28]), and the equation is sometimes called the SIRS model. The same implication has also been employed for variants of the SIR model in some studies (e.g., [22,19,8,35]). The assumption allows us to understand basic mechanisms of disease models clearly, and the aforementioned studies have provided a lot of important observations we now rely on.…”

Section: Composition Of the Functionsmentioning

confidence: 99%

Input-to-state stability and Lyapunov functions with explicit domains for SIR model of infectious diseases

Ito¹

2021

DCDS-B

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Section: Composition Of the Functionsmentioning

confidence: 99%

Input-to-state stability and Lyapunov functions with explicit domains for SIR model of infectious diseases

Ito¹

2021

DCDS-B

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“…where t s denotes the stop time of the lockdown still represented by the infection rate (15), and where a LD is given by Eq. (15). The infection rate after t s is assumed to be…”

Section: Appendix H: Modeling Of Lockdown Liftingmentioning

confidence: 99%

“…The SIR system is the simplest and most fundamental of the compartmental models and its variations. [3][4][5][6][7][8][9][10][11][12][13][14][15] The considered population of N 1 persons is assigned to the three compartments s (susceptible), i (infectious), or r (recovered/removed). Persons from the population may progress with time between these compartments with given infection (a(t)) and recovery rates (µ(t)) which in general vary with time due to non-pharmaceutical interventions taken during the pandemic evolution.…”

mentioning

confidence: 99%

“…Moreover, the initial constant infection rate a 0 characterizes the Covid-19 virus: if we adopt the German values a 0 58 days −1 and t b 11 determined below, with the remaining two parameters q and t a we can represent with the chosen functional form (15) four basic types of reductions: (1) drastic (small q 1) and rapid (t a small), (2) drastic (small q 1) and late (t a large), (3) mild (greater q) and rapid (t a small), and (4) mild (greater q) and late (t a large). The four types are exemplified in Fig.…”

mentioning

confidence: 99%

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Epidemics forecast from SIR-modeling, verification and calculated effects of lockdown and lifting of interventions

Schlickeiser

Kröger

2020

Preprint

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Due to the current COVID-19 epidemic plague hitting the worldwide population it is of utmost medical, economical and societal interest to gain reliable predictions on the temporal evolution of the spreading of the infectious diseases in human populations. Of particular interest are the daily rates and cumulative number of new infections, as they are monitored in infected societies, and the influence of non-pharmaceutical interventions due to different lockdown measures as well as their subsequent lifting on these infections. Estimating quantitatively the influence of a later lifting of the interventions on the resulting increase in the case numbers is important to discriminate this increase from the onset of a second wave. The recently discovered new analytical solutions of Susceptible-Infectious-Recovered (SIR) model allow for such forecast and the testing of lockdown and lifting interventions as they hold for arbitrary time dependence of the infection rate. Here we present simple analytical approximations for the rate and cumulative number of new infections.

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“…The present investigation can be extended to the many variants of the SIR model. [13][14][15][16][17][18][19][20][21]…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution of the SIR-Model for the Temporal Evolution of Epidemics. Part A: Time-Independent Reproduction Factor

Kröger

Schlickeiser

2020

Preprint

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We revisit the Susceptible-Infectious-Recovered/Removed (SIR) model which is one of the simplest compartmental models. Many epidemological models are derivatives of this basic form. While an analytic solution to the SIR model is known in parametric form for the case of a time-independent infection rate, we derive an analytic solution for the more general case of a time-dependent infection rate, that is not limited to a certain range of parameter values. Our approach allows us to derive several exact analytic results characterizing all quantities, and moreover explicit, non-parametric, and accurate analytic approximants for the solution of the SIR model for time-independent infection rates. We relate all parameters of the SIR model to a measurable, usually reported quantity, namely the cumulated number of infected population and its first and second derivatives at an initial time t=0, where data is assumed to be available. We address the question on how well the differential rate of infections is captured by the Gauss model (GM). To this end we calculate the peak height, width, and position of the bell-shaped rate analytically. We find that the SIR is captured by the GM within a range of times, which we discuss in detail. We prove that the SIR model exhibits an asymptotic behavior at large times that is different from the logistic model, while the difference between the two models still decreases with increasing reproduction factor. This part A of our work treats the original SIR model to hold at all times, while this assumption will be released in part B. Releasing this assumption allows to formulate initial conditions incompatible with the original SIR model.

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Global stability in a networked SIR epidemic model

Cited by 62 publications

References 8 publications

Input-to-state stability and Lyapunov functions with explicit domains for SIR model of infectious diseases

Input-to-state stability and Lyapunov functions with explicit domains for SIR model of infectious diseases

Epidemics forecast from SIR-modeling, verification and calculated effects of lockdown and lifting of interventions

Analytical Solution of the SIR-Model for the Temporal Evolution of Epidemics. Part A: Time-Independent Reproduction Factor

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