Numerical solution and parameter estimation for uncertain SIR model with application to COVID-19

Chen, Xiaowei; Li, Jing; Chen, Xiao; Yang, Peilin

doi:10.1007/s10700-020-09342-9

Cited by 76 publications

(33 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The SIR system is the simplest of the compartmental models used for the mathematical modeling of infectious diseases and had been solved numerically using various approaches, including Monte Carlo methods, wavelets, fuzzy control etc [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] and approximate solutions had been proposed [28,29]. The considered population of N 1 initially unrecovered/unremoved persons is assigned to the three compartments S (susceptible), I (infectious), or R (recovered/removed).…”

Section: Introductionmentioning

confidence: 99%

Analytical solution of the SIR-model for the temporal evolution of epidemics: part B. Semi-time case

Schlickeiser

Kröger

2021

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

Analytical solution of the SIR-model for the temporal evolution of epidemics: part B. Semi-time case

Schlickeiser

Kröger

2021

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

“…For instance, Liu (2020a) used uncertain regression analysis to forecast the cumulative numbers of COVID-19 infections in China, while Ye and Yang (2020) used uncertain time series. Following that, Chen et al (2020) presented an uncertain SIR model, and Jia and Chen (2020) proposed an uncertain SEIAR model by employing high-dimensional uncertain differential equations.…”

Section: Introductionmentioning

confidence: 99%

Initial value estimation of uncertain differential equations and zero-day of COVID-19 spread in China

Lio

Liu

2020

Fuzzy Optim Decis Making

View full text Add to dashboard Cite

Assume an uncertain process follows an uncertain differential equation, and some realizations of this process are observed. Parameter estimation for the uncertain differential equation that fits the observed data as much as possible is a core problem in practice. This paper first presents a problem of initial value estimation for uncertain differential equations and proposes an estimation method. In addition, the method of moments is recast for estimating the time-varying parameters in uncertain differential equations. Using those techniques, a COVID-19 spread model based on uncertain differential equation is derived, and the zero-day of COVID-19 spread in China is inferred.

show abstract

“…In case of temporal wave distributions with an apparent peak the half-early-peak law (30) provides an important test for the derived parameters of the wave as it relates directly the monitored quantities J(0) = J(τ = 0), J 0 = J(τ m ), j 1/2 , j max and c 3 τ m /2, where the latter can also be written in terms of the ratio between peak time τ m and early doubling time…”

Section: E Half-early-peak Lawmentioning

confidence: 99%

Forecast for the second Covid-19 wave based on the improved SIR model with a constant ratio of recovery to infection rate

Kröger¹,

Schlickeiser²

2021

Preprint

View full text Add to dashboard Cite

We start out by deriving simple analytic expressions for all measurable amounts of cases and fatalities during a pandemic evolution exhibiting multiple waves, described by the semi-time SIR model. The approximant shares all relevant features with the exact solution, including time and position of the peak of daily new infections, as well as the asymptotic behaviors at small and large times. We derive exact analytic expressions for the early doubling time, late half decay time, and a half-early peak law, characterizing the dynamical evolution. We show, in particular, how the asymmetry of the first epidemic wave and its exponential tails are affected by the initial conditions; a feature that has no analogue in the all-time SIR model. We apply the approach to available data from different continents. Our analysis reveals that the immunity is very strongly increasing during the 2nd wave, while it was still at a very moderate level of a few percent in several countries at the end of the first wave. The wave-specific SIR parameters describing the infection and recovery rates we find to behave in a similar fashion, while their ratio k was decreasing only by a about 5% for most countries. Still, an apparently moderate change of k can have significant consequences for the relevant numbers like the final amount of infected or deceased population. As we show, the probability for an additional wave is however low in several countries due to the fraction of immune inhabitants at the end of the 2nd wave, irrespective the currently ongoing vaccination efforts. We compare with alternate approaches.

show abstract

Numerical solution and parameter estimation for uncertain SIR model with application to COVID-19

Cited by 76 publications

References 20 publications

Analytical solution of the SIR-model for the temporal evolution of epidemics: part B. Semi-time case

Analytical solution of the SIR-model for the temporal evolution of epidemics: part B. Semi-time case

Initial value estimation of uncertain differential equations and zero-day of COVID-19 spread in China

Forecast for the second Covid-19 wave based on the improved SIR model with a constant ratio of recovery to infection rate

Contact Info

Product

Resources

About