# Health Sufficiency Indicators for Pandemic Monitoring

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## Abstract

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## 1. Introduction

## 2. Pandemic Monitoring

- Occupancy rate of total ICU beds (overall and for COVID-19 patients).
- Number of registered visits to primary care.
- Measles incidence and proportion of all cases among unvaccinated children whose first dose of the MMR (Measles, Mumps, Rubella) vaccine was during the COVID-19 pandemic.
- Diphtheria-tetanus-pertussis (DTP)-3 vaccination coverage in children under 12 months of age.

- The base case reproduction number, ${R}_{0}$: represents the average number of people to whom one infected person transmits the infection, during their infectious period, in a population with no immunity and no specific infection control measures.
- The effective reproduction number, $R\left(t\right)$: represents the average number of people at time t to whom an infected person transmits the infection during his or her infectious period, in a population without immunity and without specific infection control measures.

## 3. Materials and Methods

#### 3.1. Definitions

- $Confirme{d}_{t}$: Number of accumulated cases confirmed through a medical test to date t.
- $Death{s}_{t}$: Number of accumulated deaths of previously confirmed patients to date t.
- $Recovere{d}_{t}$: Number of accumulated recoveries of previously confirmed patients to date t.

- $HospitalBedOccupanc{y}_{t}$: Number of occupied beds in hospital ward due to the disease on date t
- $ICUBedOccupanc{y}_{t}$: Number of occupied beds in the ICUs of hospitals due to the disease on date t.
- $HospitalDischarg{e}_{t}$: Number of hospital discharges of previously confirmed cases on date t.
- $PrimaryCareDischarg{e}_{t}$: Number of discharges in the primary health care system of previously confirmed cases on date t.
- $HospitalBedCapacity$: Total number of beds in hospital wards, including beds in the Intensive Care Units (ICUs).
- $ICUBedCapacity$: Total number of beds in ICUs.

- $Solve{d}_{t}=Recovere{d}_{t}+Death{s}_{t}$: the accumulated number of confirmed cases with known outcomes, that is, those cases that have been solved to date t (either due to a recovery or death).
- $DailyConfirme{d}_{t}=Confirme{d}_{t}-Confirme{d}_{t-1}$, number of new daily confirmed cases on date t.
- $DailyDeath{s}_{t}=Death{s}_{t}-Death{s}_{t-1}$: number of new deaths on date t.
- $DailyRecovere{d}_{t}=Recovere{d}_{t}-Recovere{d}_{t-1}$: number of new recoveries on date t.
- $DailySolve{d}_{t}=DailyRecovere{d}_{t}+DailyDeath{s}_{t}$: number of cases that have been solved on date t.
- $ActiveCase{s}_{t}=Confirme{d}_{t}-Death{s}_{t}-Recovere{d}_{t}$: number of active confirmed cases of the disease at the end of date t. That is, number of patients with the disease at the end of date t. It comprises the count at the end of date t since the counting include the new cases on date t but not the new deaths and neither the recovered.
- $PreActiveCase{s}_{t}=ActiveCase{s}_{t-1}$: number of active confirmed cases of the disease at the beginning of date t. That is, number of patients with the disease at the beginning of date t.

- $DeathsPercentag{e}_{t}=\frac{Death{s}_{t}}{Confirme{d}_{t}}\times 100$: percentage of accumulated deaths to date t.
- $RecoveredPercentag{e}_{t}=\frac{Recovere{d}_{t}}{Confirme{d}_{t}}\times 100$: percentage of accumulated recoveries to date t.

#### 3.2. Health Sufficiency Indicators

- If $DailySolve{d}_{t}=0$ but $DailyConfirme{d}_{t}\ne 0$, then$$dHS{I}_{t}=\frac{1}{DailyConfirme{d}_{t}+1}$$
- If $DailySolve{d}_{t}\ne 0$ but $DailyConfirme{d}_{t}=0$, then$$dHS{I}_{t}=DailySolve{d}_{t}+1$$
- If $DailySolve{d}_{t}=0$ and $DailyConfirme{d}_{t}=0$, then$$dHS{I}_{t}=1$$

#### 3.2.1. Properties of the $HSI$

**Proposition**

**1.**

**Proof.**

**Proposition**

**2.**

**Proof.**

#### 3.2.2. Interpretation of the $HSI$

- $dHS{I}_{t}>1$ and $dHS{I}_{t}>\frac{aHS{I}_{t-1}}{100}$⟶ good scenario.
- $\frac{aHS{I}_{t-1}}{100}<dHS{I}_{t}<1$⟶ ordinary scenario.
- $dHS{I}_{t}>\frac{aHS{I}_{t-1}}{100}$⟶ bad scenario.

#### 3.3. Potential Occupancy Ratios

## 4. Results

#### 4.1. Local Case

- Automatic detection of the actual phase: increase, decrease or valley. The system is inspired by the Adaptive Windowing (ADWIN) method for change detection [23] and the Trent Segmentation Algorithm (TSA) [24], a linear segmentation algorithm based on the idea of looking for feature points where extreme changes on the data trend occurs. The ADWIN method uses two adaptive windows for the distribution drift, which leads to a slow detection of gradual changes. To solve this handicap, three fixed windows are selected, in order to achieve the early detection of the curve shift. In each window, a simple regression linear model is adjusted, where the slope of each line represents the growth rate of the variable response (hospital wards or ICU beds), on its current window. The slopes represent the different phases, according to their value: slope greater than zero corresponds to increase phase, less than zero corresponds to decrease, and finally zero corresponds to valley phase. For each slope of the three windows, we have one local prediction, and the final phase estimation is obtained by voting. In the case of three different phase local prediction, the middle window corresponding slope is the selected global estimation. The three windows length are based on the incubation period of COVID-19 [25]. Therefore, the lengths of big, middle and small windows are 10, 5 and 3 days, respectively.
- Automatic selection of the exogenous variables that are correlated with the corresponding target and so, might help in the prediction accuracy. In this step, the linear correlation among all exogenous variables differentiated and the target are estimated. First, all the variables which are not significantly correlated (using $\alpha =0.05$) are removed. Second, the correlation among those remaining explanatory variables is analysed in order to avoid co-linearity. If some of the variables present a significant linear relationship, the one showing a higher correlation with the rest of variables is deleted. This is repeated until there is no co-linearity among the final selected exogenous variables.
- Training of a Dynamic ARIMA model [26] with the selected explanatory variables as exogenous variables. For each prediction date, the best ARIMA model is automatically fitted. Hence, the ARIMA parameters are dynamic along the time. For each forecast horizon $Hz=1$ and $Hz=4$, the selected explanatory variables from the previous step are included into each fitted ARIMA model with lags $Hz$ and $Hz+1$. One exogenous variable is created for each explanatory variable and each lag order. A backward selection method is applied to the set of regressor variables so that only those statistically significant for the fitted ARIMA model remain.

#### 4.2. Country Case

- Balanced health resources: high health sufficiency and high potential occupancy. This is the most desirable scenario.
- Imbalanced health resources: either high health sufficiency and low potential occupancy, or low health sufficiency and high potential occupancy.
- Insufficient health resources: low health sufficiency and low potential occupancy. This is the most unfavourable scenario.

#### 4.3. International Case

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

aHSI | Accumulated Health Sufficiency Indicator |

CFR | Case Fatality Rate |

dHSI | Daily Health Sufficiency Indicator |

hPOR | Potential Occupancy Ratio |

HSI | Health Sufficiency Indicator |

icuPOR | ICU Potential Occupancy Ratio |

ICUs | Intensive Care Units |

IFR | Infection Fatality Rate |

POR | Hospital Potential Occupancy Ratio |

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**Figure 4.**Observed values (dark blue) and prediction results (light blue) for the hospital ward bed occupancy in La Rioja with 2 different forecasting horizons.

**Figure 5.**Observed values (dark orange) and prediction results (light orange) for the ICU bed occupancy in La Rioja with 2 different forecasting horizons.

**Figure 7.**Evolution of Health Sufficiency Indicators and Potential Occupancy Ratios for four regions in Spain: Castile and Leon (pink), A. C. Ceuta (blue), C. Madrid (red) and Extremadura (green).

**Figure 8.**Evolution of the different regions of Spain in terms of health sufficiency and potential occupancy.

**Figure 11.**Accumulated Health Sufficiency Indicator in most affected European, Asian and American countries.

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**MDPI and ACS Style**

Moguerza, J.M.; Perelló Oliver, S.; Martín de Diego, I.; Aceña, V.; Lancho, C.; Cuesta, M.; González Fernández, C.
Health Sufficiency Indicators for Pandemic Monitoring. *Int. J. Environ. Res. Public Health* **2021**, *18*, 5358.
https://doi.org/10.3390/ijerph18105358

**AMA Style**

Moguerza JM, Perelló Oliver S, Martín de Diego I, Aceña V, Lancho C, Cuesta M, González Fernández C.
Health Sufficiency Indicators for Pandemic Monitoring. *International Journal of Environmental Research and Public Health*. 2021; 18(10):5358.
https://doi.org/10.3390/ijerph18105358

**Chicago/Turabian Style**

Moguerza, Javier M., Salvador Perelló Oliver, Isaac Martín de Diego, Víctor Aceña, Carmen Lancho, Marina Cuesta, and César González Fernández.
2021. "Health Sufficiency Indicators for Pandemic Monitoring" *International Journal of Environmental Research and Public Health* 18, no. 10: 5358.
https://doi.org/10.3390/ijerph18105358