Pandemic Forecasting by Machine Learning in a Decision Support Problem

Abstract

This paper presents an approach that allows us, based on fairly simple models, to propose a methodology for predicting the decision of the governing bodies on the number of medical centers (MCs) required to combat a pandemic. This approach is based on the idea that the decision to open a new center is not made immediately when the existing centers are overwhelmed, but with a delay. Thus, the government aims to minimize the risks of opening MCs unnecessarily and makes this decision with the understanding that the congestion of existing centers will not end in the short term. This decision can be predicted by training the model on the historical data obtained from open sources. We develop a model that can be trained on historical data and allows forecasting the number of MCs based on a forecast of the number of hospitalized patients over a period of 14 days. Approaches are proposed for sufficiently accurately predicting the number of hospitalized patients for the model to predict the number of MCs. The models are tested on the data from open sources obtained for Ryazan oblast. For the model of forecasting the number of open MCs in Ryazan oblast, penalty functions are determined and the corresponding coefficients are calculated.

INTRODUCTION

The SARS-COVID-19 pandemic is undoubtedly still a serious challenge not only for modern medicine but for science in general. Centers for annual monitoring of the situation have appeared. These centers not only collect statistics but also determine their accuracy. These data are widely used both for high-profile headlines, decision-making, and for the scientific community to be able to analyze and predict the dynamics of the situation.

Currently, the information supplied by medical organizations and government agencies is the main source of information [1–3]. As a result, information will be similar in almost all aggregators. Nevertheless, there are errors in the statistical information received from the authorities. The most reputable aggregators check the information received from various sources and try to assess its plausibility. These aggregators include Our World in Data [4, 5] and Worldometer [6]. These global aggregators collect statistics on the total number of cases, recoveries, and deaths, as well as the number of vaccinated, tested, and hospitalized cases. At the same time, data is aggregated by countries, and to identify relative indicators, the population of these countries is taken into account.

It states that the statistics are inaccurate and may vary between countries and even counties/states. Thus, Worldometer [6] writes that a parameter such as number of recovered patients is inaccurate since it is based on different definitions. WHO recommends following the following criteria: symptoms have cleared + 2 negative tests within 24 hours or symptoms disappear + an additional 14 days; however, this is only a recommendation. In some countries, when a patient is discharged from hospital, they are considered to have recovered even if the test is not carried out. Some health officials now believe that anyone who has been diagnosed with COVID-19 three or more weeks ago and has not died has recovered from the disease. Taking this into consideration, the indicator active cases, which depends on the number of recoveries, may depend on this inherent flaw in counting the number of recoveries, both in many countries and for the entire world. Active cases = (total cases) – (total deaths) – (recovery cases). This figure represents the current number of people who have been identified and confirmed to be infected with the virus. It can increase or decrease and is an important indicator for public health and emergency response authorities when assessing hospitalization needs.

Our World in Data also considers the issue of determining the number of cases [4]. In epidemiology, cases of COVID-19, like other diseases, are broadly defined under a three-tier system:

1. The case is considered suspected when clinical signs and symptoms of COVID-19 appear, but there were no laboratory tests.

2. Probable case. A suspected disease with an epidemiological link to a confirmed case. This means that someone is showing symptoms of COVID-19 and has either been in close contact with a positive patient or is in an area particularly affected by COVID.

3. A confirmed case is “an individual with laboratory confirmation of the COVID-19 infection,” as the World Health Organization (WHO) explains. Generally, a person must have a positive laboratory test to confirm a case. This is true whether they show symptoms of COVID-19 or not.

To estimate the extent of an outbreak, we need to know the actual number of infections, but the actual number of cases depends on the number of tests carried out, and increased testing of the population will increase the number of confirmed cases, and the number of cases will steadily increase. This approach to collect statistics makes it heterogeneous. Frequent testing of medical personnel and rare testing of groups of citizens who are not required to be tested distorts the incidence statistics. However, these data can be used for cases of hospitalization, since during hospitalization the patient is almost always tested for PCR.

The mortality rate from COVID-19 is also controversial. Often, patients die from comorbidities even though they have been cured of COVID-19, and sometimes vice versa. This is due to the rules for diagnosing the cause of death, which can vary. In addition, pandemic diseases impose additional requirements on medical personnel, which leads to political decisions regarding the maintenance of a patient’s medical record and the procedures performed.

As a result, an indicator such as active cases does not accurately describe the current state of affairs, and it is incorrect to determine the number of potential patients based only on this indicator. Nonetheless, this statistic is used by governments for decision-making despite having a fairly high level of errors. This statistic can be used to make management decisions since they are determined on the dynamics and complex state of the situation rather than one indicator.

In Russia, management decisions on opening new departments within existing medical centers (MCs) are made locally or at the regional level. Moreover, apart from specialized centers for combating the pandemic, these decisions are made based on regional statistics [2] and the statistics within one MC. The number of hospitalized patients by district can be estimated by estimating the ratio of the number of patients hospitalized to the number of cases calculated throughout Russia. Due to the uniform requirements and rules for the hospitalization of patients, it can be assumed that this assessment will be sufficiently reliable. We will take information on the number of hospitalized patients from the Worldometers aggregator [6]. Complete information on Russia is not available, but there are several countries (the ISO country codes are indicated) that indicate the number of patients hospitalized weekly. The ratios of the number of hospitalized cases to the total number of new cases of the disease weekly_hosp_admissions/Σ_7daysnew_cases (parameters of the Worldometers aggregator) are presented in Fig. 1. The figure shows that the value of the indicator after October 2020 remains stable (except for the surge in Israel). For this statistic, we determine the confidence intervals of the mathematical expectation of the percentage of hospitalized patients with a confidence probability of 0.95 (Fig. 2). At the initial stage, PCR testing was carried out mainly to confirm symptoms and diagnosis, mainly in medical institutions, and therefore the percentage of hospitalizations is high: more than 15%. Subsequently, testing has become a requirement in relation to many activities and in some countries it has become comprehensive. As a result, patients began to be identified who did not require hospitalization due to the absence of severe symptoms. As a result, the percentage of hospitalized cases first fell to 7.5% and later fell below the 5% mark of the total number of cases. This indicator is also close to the indicator of the official information aggregator for Russia [1].

Fig. 1.

Ratio of hospitalized patients to total new cases for the following countries: Belgium, Czech Republic, France, Germany, Israel, Italy, and the United Kingdom.

Fig. 2.

Mean value and confidence interval of the ratio of the number of hospitalized patients to the total number of new cases.

These values can be used to estimate the number of hospitalized people in the country. These figures help to make administrative decisions at the government level. To analyze the estimated level of hospitalization required for a particular region or medical institution, we need to take the statistics of detected cases of diseases taken from the Our World in Data aggregator [5] for a certain region, for example, in Ryazan oblast, and determine the volume of hospitalization using the parameter confirmed cases. Using this coefficient, it is possible to estimate the volume of new admissions to medical institutions. However, at the same time, this indicator does not determine how many patients will be admitted to medical institutions.

The Our World in Data aggregator also provides information on the number of active cases, i.e., the total number of patients with COVID-19 on a given date. The website of the Government of Ryazan oblast [2] contains information on the number of patients admitted to medical institutions. Based on the available information, it is possible to calculate the ratio that determines the percentage of patients undergoing treatment in MCs to the number of cases of COVID-19 (Fig. 3). The coefficient does not fall below 10%, since the time spent in a medical institution is taken into account. At its peak, half of all COVID-19 patients were in healthcare facilities. These peaks are related to the delay in discharging a patient from a medical institution compared to recovery at home.

Fig. 3.

The ratio of the number of patients who are hospitalized to the total number of cases in the Ryazan region.

Figure 4 shows graphs of the number of patients (dashed-dotted line, right axis) and hospitalized patients (solid line, left axis). The solid line clearly shows the marginal possibilities of hospitalization. These are 220, 450, 660, 900, and more than 1250 patients. The volume of 220 patients determines the number of patients who can comfortably be looked after at MCs. With a decrease in the number of patients, additional hospitalization in mild cases of the disease is possible. The volume of 450 determines the load limit of the existing departments. The growth of diseases in May–June 2021 reached the limit (June 28–29) with 450 hospitalized cases. Next, a new center needed to be opened, which began to fill up quickly. As a result, on July 3, the number of hospitalized people increased by 154 and a week later reached the next mark of 660 people. However, the number of cases increased, and the load on the existing departments did not decrease. As a result, more departments are being opened (October 16, 2021 (900 patients) and November 2, 2021) and the number of hospitalized patients has reached 1250.

Fig. 4.

The number of infected and hospitalized patients in Ryazan oblast.

This study develops a model for predicting the number of required MCs for a period of more than 14 days. The number of health centers can be described using specific centers represented as a dataset. For all operating MCs, it is possible to describe the number of beds, i.e., the volume of patients that this MC can accept. Based on the data obtained, it is possible to calculate the possibilities of the region in terms of hospitalization and compare these possibilities with the real and predicted situation.

Since a discrete problem of a small volume is actually being solved, the predictive values may be inaccurate. A model is being developed that determines the predictive value of open MCs based on the forecast of the number of hospitalized patients. The forecast value of hospitalized patients is determined based on the forecast models and data obtained from open aggregators and official sources.

FORECASTING METHODS USED TO ANALYZE THE PANDEMIC

Modern works related to machine learning are primarily aimed at diagnosing the disease, most often by analyzing radiographs [7–10]. In [11], it is proposed to apply multivariate linear regression to predict the number of cases of COVID-19 within 14 days. The calculations are checked using a precise measure such as the mean absolute error (MAE) or root mean square error (RMSE) for the most affected regions around the world. In [12], historical data were predicted using exponential smoothing to identify patterns of seasonality and confidence intervals surrounding each predicted value. In [13], various data sources and the possibility of predicting the number of diseases based on different information are considered. The SEIRD model is often used for analysis [11, 14–17]. The SEIRD epidemic model belongs to the class of so-called compartmental models, the core of which is to divide the population into several compartments, which in our case consists of the following compartments: susceptible, exposed (the disease is in the incubation period), infectious (sick), recovered, and dead. Then the size of each of the compartments is compared with a variable in the system of differential equations, by solving which, it is possible to predict the dynamics of the epidemic. There are quite a few modifications of the SEIRD model, for example, SEIR is a simplified model that does not take into account cases of recovery and death separately.

The work [18] provides a set of methods and models used to analyze and predict various situations related to the development of COVID-19. The paper notes the methods of analysis and forecasting related to a large set of data, including atmospheric parameters and information in social networks. Nevertheless, the paper notes a positive trend in the application of restrictive measures. The work of Xiaolin Zhu et al. [19], which presents a spatial pandemic model for predicting the number of deaths. This study aims to create a predictive model that will analyze the growth of the virus over the following month, given the current dynamics of COVID-19. However, the proposed methods are usually less accurate than classical methods based on statistics. The proposed models perfectly predict the following days, but the forecast for a week or a month is no longer as accurate. At the same time, the issues of predicting the volume of patient hospitalizations from the point of view of the work of medical institutions are not considered. For such a model, a forecast for a couple of days will be of little use. However, anticipating the possibility of opening a new department the following month allows us to plan supplies and hire the staff required.

MODEL DESCRIPTION

Usually, the quality criteria of supervised machine learning models are indicators that characterize the accuracy of the forecast. However, in terms of decision support tasks, the simulation results should contribute to attaining the quality criteria for the decisions taken. Of course, good forecast accuracy should ensure the construction of good decision-making models; however, in the context of some problems with small or indirect statistics, for example, forecasting the consumption of new goods and forecasting pandemics, good forecast accuracy is unattainable and it is advisable to move on to criteria that characterize the quality of management decisions obtained based on the forecast. Another problem with widely used precision criteria is their symmetry. However, in many problems, positive and negative errors have different implications for decisions based on predictions. For example, we consider the forecast of the required stocks of medicines: if the forecast is overestimated, then we can spend unnecessary financial resources, which is certainly not very good, but if the forecast is underestimated, then we can lose human lives, which is clearly more critical.

A model aimed at determining the predictive value of open MCs at a certain point in time is considered. The parameters of such a model are a set of MCs located in a particular county or region. Each MC has a certain capacity, which is not necessarily the same, , . For convenience, we can represent a set of MCs as an array of Boolean values. Moreover, , , if the MC is in operation and admitting patients infected with a pandemic illness.

As part of the study, it is proposed to build a mathematical model to determine the predictive value of operating MCs for more than two weeks with certain possibilities of hospitalization ().

The forecast is supposed to be built based on the forecast of the number of patients in MCs . The initial data of such a model can be historical data on the number of infected patients (I) and hospitalized patients (P). The main features of the proposed model are as follows:

1. There is an existing infrastructure that operates normally and can provide a certain volume of hospitalization ((, ).

2. For a healthcare facility, there is a volume of hospitalization related to normal operation (); usually this is less than the maximum possible volume (often half the officially declared maximum capacity) (). Thus, almost immediately, the departments are filled to the normal volume, and in the event of an increase in the number of cases, a further increase occurs up to the maximum volume of hospitalization.

3. If new departments are opened when the maximum level of hospitalization has been reached, then the new departments are quickly filled with patients.

4. New departments are opened if the maximum level of patients is kept for a certain time. In June 2020, the first peak (450 patients) lasted 22 days and did not lead to the opening of a new department. The second peak from October 2020 to February 2021 lasted 225 days. Twenty-seven days after reaching the maximum in October 2020, the number of departments, which remained in operation until February, was increased. In June–July 2021, the maximum volume lasted 12 days, after which new departments were opened.

The task on which the proposed approach was tested is the analysis of the necessary support for the departments. This applies to the purchase of consumables and hiring staff. The abrupt opening of a new department is inefficient in terms of purchasing consumables, as not all materials can be delivered by the time the department is opened and they can be purchased at inflated prices. This problem can be solved using machine learning methods.

The initial data of the task are as follows:

(1) information about MCs: , , , ;

(2) information about the historical data on the operation of the centers , where N is the volume of historical data):

(a) is the total number of cases at time t;

(b) is the total number of hospitalized patients at time t;

(c) are the MCs at time t in which patients have been hospitalized.

As a result, for each moment of time , it is necessary to determine the predictive value of the operating MCs (). This parameter is determined based on the predicted value of the number of hospitalized patients () and machine learning. Since the expansion of existing MCs is a management decision and depends not just on the volume of patients, the predicted number of MCs will be determined not only by their capabilities but also by historical information on the speed with which they were opened.

As part of machine learning, it is proposed to use quantile regression. It is necessary to define penalty functions that can be used to evaluate the accuracy of the forecast. Since it is necessary to predict the volume of supplies and the number of working departments of the MC, it is necessary to impose a fine for a lack of funds and MCs to service all cases of the disease. At the same time, with the normal functioning of the departments, planning of new deliveries is not required. However, with an increase in the number of patients, the load on MCs grows and the penalty function should also increase. When the maximum possible volume is reached, it is necessary to open a new department if the number of patients grows. For opening a department without resources, a maximum penalty must be set. It is recommended to purchase materials and train staff a month before the opening of the department. It is also necessary to consider the possibility of purchasing a small volume of consumables and storing them in working departments. The general form of the penalty function calculated based on the estimate of the current number of hospitalized patients (), as well as the normal () and maximum () capacity of medical institutions, is given below:

1

2

3

Here, is an estimate of the number of hospitalized patients, which can be obtained as a linear combination of the forecast and data from official sources (if available). The predicted value is determined based on the total number of cases and the predicted number of cases, taking into account the hospitalization rate. determines the number of hospitalized patients who medical facilities can admit during normal operation t days earlier. This value is determined by the capabilities of MCs and is calculated as the sum of the capabilities of all MCs in the area, including newly opened ones. determines the maximum capacity of medical facilities t days earlier. We can use the estimate ; α are the coefficients of the degree of the penalty function. It is recommended to use ; ; and . Coefficients w1 and w2_t define specific dependences for the penalty function: expresses the depth of historical data, i.e., how many previous days (measurements) to take into account in the forecast. is the significance of historical data. Coefficients and distinguish certain practices of the work of government bodies in opening new departments. These data may differ in different regions and therefore the penalty function for each region must be compiled separately. We can use machine learning and gradient descent method to calculate coefficients . To reduce the dimension of the problem (if we analyze the monthly history, we need to calculate more than 30 weights), we can combine the weight coefficients into blocks.

It is proposed to train and test the model based on the available data from official sources and using the official data on the number of hospitalizations instead of predictive ones. Based on the results of optimization, the number of operating MCs at time t and parameters of the normal () and maximum () capacity of MCs change in such a way as to provide the required volumes of hospitalization.

MODEL RESULTS

We will evaluate the operation of the model based on the data obtained from official sources of Ryazan oblast [2]. In Ryazan oblast, there is a main hospitalization center for COVID-19 with 225 beds with a maximum load of 450. A second center allows increasing the number of beds up to 350; and the maximum number, up to 650. Two more centers with 300 beds (maximum value) can be opened if necessary.

The model was trained on the initial data for Ryazan oblast. In the course of training, the values of the weight coefficients were determined based on the proposed penalty functions for = 30. At the same time, the parameters of the normal and maximum capacities of all open MCs were determined. In Fig. 5, lines with long dashes mark the predicted value of the maximum volume of possible hospitalization based on open MCs when predicting 14 days ahead. The graph shows that the predicted value of hospitalization volumes reflects the real volumes.

Fig. 5.

The number of infected and hospitalized patients, and the forecast of the volume of hospitalization of MCs in Ryazan oblast.

PREDICTING THE VOLUME OF HOSPITALIZATION

We need to know the number of hospitalized to use the model. It is difficult to predict this parameter, since there are no sufficiently accurate models that describe the time spent in an MC with COVID-19. For such models to work, it is possible to estimate the number of hospitalized as a certain percentage of the total number of active cases, for which mathematical models are available for prediction.

Based on the data from Our World in Data and the website of Ryazan oblast, it is possible to determine both the volume of active cases and the volume of hospitalization. The ratio of these values, which determines the volume of hospitalized patients as a percentage, is displayed in Fig. 3. The normal volume of hospitalized patients is about 20%. The peaks define a sharp increase in the number of hospitalized patients relative to the total number of patients and describe outbreaks of the pandemic. Until April 2021, the peaks on the graphs correspond to a decrease in the number of active cases. The duration of such a peak reaches 4 months. At the same time, we can say that at the peak, about 50% of the infected are being treated in MCs. According to the calculated predictive value of the number of hospitalized patients, it is possible to forecast the number of operating MCs. The accuracy of this model makes it easy to predict the number of MCs required. The prediction of active cases can be derived from well-known models, such as the SEIRD model.

Alternatively, information on the number of hospitalized patients each day can be used. This information can be found from many sources, official websites [1], from the Worldometers aggregator, etc. This parameter is stationary, as seen from Figs. 1 and 2. To use it, it is necessary to build a model for predicting the time of hospitalization of patients. As a result, it is possible to calculate the volumes of hospitalized patients based on the model for predicting the number of new cases and the estimated time of hospitalization.

CONCLUSIONS

This paper presents an approach that allows us, based on fairly simple models, to propose an approach to predict the decision of governing bodies on the number of MCs required to combat a pandemic. This approach is based on the idea that the decision to open a new center is not made immediately with the overflow of existing centers, but with some delay. Thus, the government is trying to minimize the risks of unnecessarily opening centers and makes this decision, realizing that the congestion of existing centers will not end in the short term. This decision can be predicted by training the model on the historical data obtained from open sources. The model is based on the parameter responsible for the number of hospitalized patients. Approaches are proposed that allow predicting this coefficient with sufficient accuracy for the operation of the model for predicting the number of MCs. Since management decisions depend on government regulations and available resources, this model is expected to be used to estimate future parameters in the same area in which the training was conducted.

CONFLICT OF INTEREST

The authors declare that they have no conflicts of interest.