SI epidemic model applied to COVID-19 data in mainland China

Abstract

The article is devoted to the parameters identification in the SI model. We consider several methods, starting with an exponential fit to the early cumulative data of SARS-CoV2 in mainland China. The present methodology provides a way to compute the parameters at the early stage of the epidemic. Next, we establish an identifiability result. Then we use the Bernoulli–Verhulst model as a phenomenological model to fit the data and derive some results on the parameters identification. The last part of the paper is devoted to some numerical algorithms to fit a daily piecewise constant rate of transmission.

Estimation of Daily Reproduction rates in COVID-19 Outbreak

“…The article has used a discrete approach for describing the dynamics of the Covid-19 outbreak. In the ODE SIR case [28,29,30], marginal can be estimated in the same way, but by using continuous deconvolution equation. An improvement in this framework could be the introduction of the demographic notion of age class, because the daily reproduction rates distribution is depending on the state of the immune defences both of the infected and susceptible individuals, and on the mode of transmission, this mode being associated in social settings recording age and infection schedule with more secondary cases for young and adult than for elderly at home [31,32].…”

A robust phenomenological approach to investigate COVID-19 data for France

“…The SI epidemic model used in this work is the same as in [8]. It is summarized by the flux diagram in Figure 2.…”

“…Parameters estimated in the simulations: As described in [8] the number of infectious at time t 0 is…”

“…The major difficulty here is to provide a model that gives a good description of the tendency for the data. It has been observed in our previous work that it is difficult to choose between the possible phenomenological models (see Figures 12-14 in [8]). The phenomenological model can also be viewed as a regularization of data that should not fluctuate too much in order to keep the essential information.…”

Epidemic Dynamics via Wavelet Theory and Machine Learning with Applications to Covid-19

“…However, while those use single waves coming from solutions differential equations, we use general wavelet functions such as Gaussian functions, log-normal functions, Gompertz density functions and Beta prime density functions, which all satisfy our general condition of being epidemic-fitted in the sense of Definition 2. We also refer to the works in [ 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 ] for other approaches on modelling and forecasting the spread of Covid-19 epidemic using deep learning, machine learning, time series analysis, network model, stochastic model and deterministic compartmental framework.…”