Mathematical Modeling and Epidemic Prediction of COVID-19 and its Significance to Epidemic Prevention and Control Measures

Abstract

Background Since receiving unexplained pneumonia patients at the Jinyintan Hospital in Wuhan, China in December 2019, the new coronavirus (COVID-19) has rapidly spread in Wuhan, China and spread to the entire China and some neighboring countries. We establish the dynamics model of infectious diseases and time series model to predict the trend and short-term prediction of the transmission of COVID-19, which will be conducive to the intervention and prevention of COVID-19 by departments at all levels in mainland China and buy more time for clinical trials. Methods Based on the transmission mechanism of COVID-19 in the population and the implemented prevention and control measures, we establish the dynamic models of the six chambers, and establish the time series models based on different mathematical formulas according to the variation law of the original data. Findings The results based on time series analysis and kinetic model analysis show that the cumulative diagnosis of pneumonia of COVID-19 in mainland China can reach 36,343 after one week (February 8, 2020), and the number of basic regenerations can reach 4.01. The cumulative number of confirmed diagnoses will reach a peak of 87,701 on March 15, 2020; the number of basic regenerations in Wuhan will reach 4.3, and the cumulative number of confirmed cases in Wuhan will reach peak at 76,982 on March 20. Whether in Mainland China or Wuhan, both the infection rate and the basic regeneration number of COVID-19 continue to decline, and the results of the sensitivity analysis show that the time it takes for a suspected population to be diagnosed as a confirmed population can have a significant impact on the peak size and duration of the cumulative number of diagnoses. Increased mortality leads to additional cases of pneumonia, while increased cure rates are not sensitive to the cumulative number of confirmed cases. Interpretation Chinese governments at various levels have intervened in many ways to control the epidemic. According to the results of the model analysis, we believe that the emergency intervention measures adopted in the early stage of the epidemic, such as blocking Wuhan, restricting the flow of people in Hubei province, and increasing the support to Wuhan, had a crucial restraining effect on the original spread of the epidemic. It is a very effective prevention and treatment method to continue to increase investment in various medical resources to ensure that suspected patients can be diagnosed and treated in a timely manner. Based on the results of the sensitivity analysis, we believe that enhanced treatment of the bodies of deceased patients can be effective in ensuring that the bodies themselves and the process do not result in additional viral infections, and once the pneumonia patients with the COVID-19 are cured, the antibodies left in their bodies may prevent them from reinfection COVID-19 for a longer period of time.

Determine the Best Models for Time Series by using a New Suggested Technique

“…Mixed (autoregressive-moving average) and abbreviated (ARMA (p, q)), where (p) represents the rank of the autoregressive and (q) represents the rank of the moving average. { [6], [3], [19], [21], [9]} The stationary {yt} time series is in the form ARMA(p, q) Ø(B) yt = θ (B) at…”

“…B j at = at-j {at}is a series of random errors called white noise, and the models (AR(p), (MA(q)) can be considered special cases of the model (ARMA (p, q)) from a mathematical standpoint. { [18], [13], [6], [5]}. The identification stage is important in time series analysis.…”

“…After knowing whether the type of model is AR(p), MA(q), or ARMA (p, q) and determining its rank, i.e., valuable knowledge p or q, or both, the process of estimating the model parameters is carried out using one of the estimation methods. { [6], [4]}. After estimating the parameters of the model that was identified, the examination process is carried out, and this is done through a set of tests, all of which agree with the goal, which is to test the autocorrelation function ACF for the series of estimated errors {ât} and the partial autocorrelation function PACF for the series of estimated errors and find out whether they are not significant, which means that the model is efficient and can be adopted in forecasting.…”

“…[8] The second represents data for (7) daily time series, each of which has a length of (76) representing the number of daily infections recorded for the Corona pandemic during the period from 1st March to 15th May of the year 2020 and for the countries (Iraq, Saudi Arabia, Emirates, Qatar, Kuwait, Oman, and Bahrain). { [6], [13]}.…”

Forecasting the spread of COVID-19 based on policy, vaccination, and Omicron data

“…For mathematical models, the Susceptible-Exposed-Infectious-Quarantined-Recovered (SEIQR) model was applied to predict daily confirmed cases, isolated people, and peak date of isolation during the first outbreak in Daegu, South Korea 11 . Using the number of cumulative cases, suspected, recovery, deaths, and quarantined population in mainland China, the Susceptible-Exposed-Infectious-Quarantined-Diagnosis-Recovered (SEIQDR) model was used to predict cumulative future cases, infection rate, and regeneration number of the disease 12 . However, both models were not able to cover the effects of vaccinations and the insusceptible group with immunity.…”