A stochastic SEIHR model for COVID-19 data fluctuations

Abstract

Although deterministic compartmental models are useful for predicting the general trend of a disease’s spread, they are unable to describe the random daily fluctuations in the number of new infections and hospitalizations, which is crucial in determining the necessary healthcare capacity for a specified level of risk. In this paper, we propose a stochastic SEIHR (sSEIHR) model to describe such random fluctuations and provide sufficient conditions for stochastic stability of the disease-free equilibrium, based on the basic reproduction number that we estimated. Our extensive numerical results demonstrate strong threshold behavior near the estimated basic reproduction number, suggesting that the necessary conditions for stochastic stability are close to the sufficient conditions derived. Furthermore, we found that increasing the noise level slightly reduces the final proportion of infected individuals. In addition, we analyze COVID-19 data from various regions worldwide and demonstrate that by changing only a few parameter values, our sSEIHR model can accurately describe both the general trend and the random fluctuations in the number of daily new cases in each region, allowing governments and hospitals to make more accurate caseload predictions using fewer compartments and parameters than other comparable stochastic compartmental models.

Fuzzy Clustering Methods to Identify the Epidemiological Situation and Its Changes in European Countries during COVID-19

“…Many possible approaches for this modelling can be considered, i.e., non-linear regression, Markov models, differential equation systems (continuous time), and difference equations (discrete time). There are many infectious disease-spread models, such as SIR, SIS, SIRS, SEIR, SEIRD, and SEIHR see e.g., [ 35 , 36 ]. Ivorra et al [ 31 ] developed a mathematical model for the spread of the coronavirus.…”

Summaries, Analysis and Simulations of Recent COVID-19 Epidemics in Mainland China

“…Assume that after day 90 (March 31, 2022), it still keeps the transmission rates β ′ ij s, the blocking rates Θ 1 (11), Θ 2 (11)), the recovery rates κ (11), and κ a (11)) until day 100 (10 April, 2022). The simulation results of equation (3.1) are shown in Fig.…”

“…Furthermore assume that after day 90 (March 31, 2022), it still keeps the transmission rates β ′ ij s, and recovery rates (κ (11), κ a (11)) but increases the blocking rates to (Θ 1 , Θ 2 ) = (99%, 99%) until day 100. The simulation results of equation (3.1) are shown in Fig.…”

“…Modelling the dynamics of spread of disease can help people to understand the mechanism of epidemic diseases, formulate and evaluate prevention and control strategies, and predict tools for the spread or disappearance of an epidemic [2]. Since the outbreak of COVID-19 in Wuhan China, a large numbers of articles on modelings and predictions of COVID-19 epidemics have been published (for examples see [3][4][5][6][7][8][9][10][11]).…”

Preface

“…This problem is considered in [7,8] for China and Italy, respectively. Other interesting model refinements include time-varying models [9], time delays [10] and stochasticity [11,12].…”