A Time-Dependent SIR Model for COVID-19 With Undetectable Infected Persons

Abstract

In this paper, we conduct mathematical and numerical analyses for COVID-19. To predict the trend of COVID-19, we propose a time-dependent SIR model that tracks the transmission and recovering rate at time t. Using the data provided by China authority, we show our one-day prediction errors are almost less than 3%. The turning point and the total number of confirmed cases in China are predicted under our model. To analyze the impact of the undetectable infections on the spread of disease, we extend our model by considering two types of infected persons: detectable and undetectable infected persons. Whether there is an outbreak is characterized by the spectral radius of a 2 Â 2 matrix. If R 0 > 1, then the spectral radius of that matrix is greater than 1, and there is an outbreak. We plot the phase transition diagram of an outbreak and show that there are several countries on the verge of COVID-19 outbreaks on Mar. 2, 2020. To illustrate the effectiveness of social distancing, we analyze the independent cascade model for disease propagation in a configuration random network. We show two approaches of social distancing that can lead to a reduction of the effective reproduction number R e .

Real-Time Estimation of Rt for Supporting Public-Health Policies Against COVID-19

“…In terms of the parameters of the SIR model, we can calculate R t as the ratio between the time-dependant infection and recovery rates, β( t ) and γ( t ), respectively ( 1 , 9 ), multiplied by the probability of finding a susceptible individual :…”

“…Several mathematical models to fit public databases on the SARS-CoV-2 outbreak have recently been proposed (1)(2)(3)(4). Despite their particularities, a great part share the same compartmental structure, inspired on the well-known SIR model (5).…”

“…Similarly, for later stages, compartmental mathematical models have been used to infer the virus's spreading rate and subsequently calculate the reproduction number ( 14 – 16 ). Chen et al ( 1 ) uses a time-dependant SIR-model, where the different involved rates are allowed to change over time. After numerically finding the value that minimizes a curve-fitting functional, they evaluate the basic reproduction number considering two types of spreaders.…”

Investigating Epidemic Growth of COVID-19 in Saudi Arabia based on Time Series Models

“…Prior studies that have noted the importance of using various mathematical models for predicting the spread of COVID-19 pandemic are different. Most of these studies have been established based on time series models [13][14][15][16][17][18][19][20], and other studies have been based on differential equations models [5] [21][22][23]. However, very little effort was found in the literature on the question of predicting the end of the COVID-19 outbreak in Saudi Arabia.…”

“…Also, the SIR model can be used for investigating the predicting the peak and the end of the epidemic, the effect of the asymptomatic infection on the spread of COVID-19 outbreak, herd immunity variables, and social distance parameters [18].…”