key: cord-0784786-amwz712t authors: Garrido, J.M.; Martínez-Rodríguez, D.; Rodríguez-Serrano, F.; Pérez-Villares, J.M.; Ferreiro-Marzal, A.; Jiménez-Quintana, M.M.; Villanueva, R.J. title: Mathematical model optimized for prediction and health care planning for COVID-19() date: 2022-02-28 journal: Med Intensiva (Engl Ed) DOI: 10.1016/j.medine.2022.02.020 sha: 82ba995c884475f06d51375596d37867ab242911 doc_id: 784786 cord_uid: amwz712t OBJECTIVE: The COVID-19 pandemic has threatened to collapse hospital and ICU services, and it has affected the care programs for non-COVID patients. The objective was to develop a mathematical model designed to optimize predictions related to the need for hospitalization and ICU admission by COVID-19 patients. DESIGN: Prospective study. SETTING: Province of Granada (Spain). POPULATION: COVID-19 patients hospitalized, admitted to ICU, recovered and died from March 15 to September 22, 2020. STUDY VARIABLES: The number of patients infected with SARS-CoV-2 and hospitalized or admitted to ICU for COVID-19. RESULTS: The data reported by hospitals was used to develop a mathematical model that reflects the flow of the population among the different interest groups in relation to COVID-19. This tool allows to analyse different scenarios based on socio-health restriction measures, and to forecast the number of people infected, hospitalized and admitted to the ICU. CONCLUSIONS: The mathematical model is capable of providing predictions on the evolution of the COVID-19 sufficiently in advance as to anticipate the peaks of prevalence and hospital and ICU care demands, and also the appearance of periods in which the care for non-COVID patients could be intensified. Desarrollo de un modelo matemático tipo SEIR capaz de predecir la evolución de la pandemia considerando las medidas de salud pública establecidas. Número de pacientes infectados por SARS-CoV-2, y hospitalizados e ingresados en UCI por la COVID-19. A partir de los datos registrados hemos podido desarrollar un modelo matemático que refleja el flujo de la población entre los diferentes grupos de interés en relación a la COVID-19. Esta herramienta permite analizar diferentes escenarios basados en medidas de restricción socio-sanitarias, y pronosticar el número de infectados, hospitalizados e ingresados en UCI. Coronaviruses cause respiratory and intestinal diseases in many animal species. In humans, four of these viruses produce upper airway infections (OC43, HKU1, 229E and NL63) and two can cause severe respiratory syndromes (SARS-CoV-1 and MERS-CoV) 1 The application of non-pharmacological measures such as social distancing, the wearing of face masks, the improvement of hygiene measures, lockdowns, home confinement, the closing down of non-essential services, mobility restrictions, etc., is particularly important, since they have a direct impact upon the speed with which the disease spreads 5, 6, 7 . In fact, the indicators on the evolution of COVID-19 improved noticeably in Spain two weeks after the official national lockdown declaration of 14 March 2020, and moreover showed that regions in the early stages of the pandemic at the start of lockdown (such as Ceuta and Melilla) had mortality rates far lower than regions starting with more widespread transmission, such as Catalonia. The above reflects the important differential effect of the adopted measures, provided they are introduced early 8 . In relation to the consequences derived from the population impact of COVID-19, the pandemic causes a very important decrease in the care dynamics of patients suffering from other kinds of illnesses. In order to secure adequate planning, it is necessary to use tools that can predict the evolution of COVID-19 in accordance to the starting situation and the non- The present study describes a mathematical model designed to predict the transmission dynamics of COVID-19 and the requirements referred to hospitalization and admission to the ICU. The model has been calibrated and validated using data provided by the hospitals of the province of Granada (Spain), which jointly provide healthcare for a population of 914,678 inhabitants 9 . In addition, we present estimates referred to three scenarios based on different sociosanitary containment programs. The study data were compiled from the following hospitals in the province of Granada: We implemented a susceptible, exposed, infected recovery (SEIR) model specifically designed to describe the dynamics of the pandemic at population level and at hospital circuit level in relation to patients with COVID-19 (hospital ward and ICU admissions), since this is the most limiting aspect when having to deal with the pandemic, given the material and human resources required (Fig. 1 ). Table 1 shows the different groups into which the population can be divided with respect to infection and the hospital circuit, together with the difference equations that describe the dynamics of each group over time. The transition between groups is determined by the transition rates qs, sq, li, ir, ih, iu, hu, hf, ha, uf, uhu, hf and hua. In this regard, β is the transmission rate between susceptible (S) and infected (I), and its value is proportional to the magnitude of the basic J o u r n a l P r e -p r o o f reproduction number R0, according to the expression: R0 = β/(ir + ih + iu). During the model calibration process, and drawing upon the hospital records, we were able to determine the value of the different transition rates and of the transmission rate (β) required for the model to be capable of describing the specific situation of the province of Granada, using the Novelty Swarm optimization algorithm implemented in Python3 for this purpose 10 Since the model also takes into account those subjects who have not been diagnosed, use was made of the data from the seroprevalence study of the Spanish provinces for Granada in order to calibrate the number of infected individuals 13 . To obtain robust values of the parameters, we performed 600 calibration processes that yielded the corresponding 600 sets of parameters describing the specific epidemiological situation of the province of Granada up until 22 September 2020. Based on the 600 estimations, we obtained the mean and 95% confidence interval (95%CI) of both the parameters and the predictions. After completing the calibration, we validated the model, comparing the predicted data against those recorded between 23 September and 7 November 2020, totaling 956 patients. Three scenarios were generated, contemplating non-pharmacological measures to simulate the most probable evolution of the pandemic, and to determine the most favorable conditions to conjugate the peaks and troughs referred to prevalence and to the hospitalization and ICU admission needs. The initial scenario represents the predicted evolution, taking into account the restrictions that were established for the province of Granada when it was in level 4 phase 2 of the state of alarm -this implying the temporary closing down of non-essential services, the restriction of commercial opening hours and mobility, and perimeter lockdown 14 . These measures were implemented for two weeks from 10 November 2020. In our simulations, we The developed model allowed us to establish different scenarios referred to the application of restriction measures and to foresee the evolution of the number of infected subjects, and the admissions to hospital and the ICU (Table 2) hospital and to the ICU seen in the past period of March to April 2020 (Fig. 3) . It should be noted that although hospital pressure during the first wave of the pandemic was high, the hospital services of the province did not reach the saturation point, since home lockdown was decreed when prevalence in the province was still in its early (Fig. 5) . The complex healthcare situation due to the current COVID-19 pandemic is further compounded by the important impact upon the normal functioning of medical and hospital care 16, 17, 18 , and by the high opportunity cost generated in relation to many serious disease conditions that have not been properly managed because of the pandemic. The adequate treatment and follow-up of certain groups of patients infected with SARS-CoV-2 takes on particular importance, since they present comorbidities that appear to be correlated to the need for hospital and ICU admission in the context of COVID-19, such as arterial hypertension, chronic heart diseases, diabetes, chronic lung diseases and obesity 19 . Due to the above, it is necessary to establish a joint public health strategy that should contemplate two fundamental aspects. On one hand, a COVID-19 care circuit must be developed to ensure adequate management of these patients both on an ambulatory basis and in the context of admission to the hospital or the ICU. On the other hand, a non-COVID-19 care circuit also must be established seeking to maximally reduce the opportunity cost referred to the rest of serious disease conditions, in order to curb the substantial increase in associated morbidity-mortality 30, 31, 32 . The cumulative opportunity cost of the rest of serious disease conditions during the period corresponding to the first two waves of the COVID-19 pandemic, and the healthcare institution recovery / normalization phase, evidenced the impossibility of maintaining adequate population care outside the overwhelming COVID-19 scenario. This impossibility to maintain both circuits (COVID-19 / non-COVID), even with reinforcement of the healthcare structures, is reflected by the percentage of resources directed to patients with COVID-19 33 . In addition, the ethical problem derived from polarization of the system towards management of the pandemic has constituted an important focus of debate 34, 35, 36 . The identification of the populational behavior of the virus -characterized by peaks and troughs -is of particular relevance for correct planning. Logically, and preserving quality care for urgent / emergent cases of patients with different serious disease conditions, healthcare can be organized as alternating periods of care focalization 37, 38 . Thus, during the peaks of the pandemic, attention to COVID-19 would be intensified, reducing the care of stable patients with other diseases in proportion to the magnitude of the peaks of the pandemic. In contrast, during the trough periods, clinical activity targeted to non-COVID-19 disease would be intensified to above standard levelstaking full advantage of the window of opportunity provided. In this sense, the mathematical model presented in this study could make an In addition, the model has a modular construction, making it possible to incorporate other groups with the appearance of new factors that exert an important influence upon the dynamics of viral transmission, such as a SARS-CoV-2 vaccination campaign 39 , and its associated percentage efficacy. Community or herd immunity would be defined as 1 -(1 / R0) 40 . Taking into account the contagion rates obtained through calibration of the model, without the application of drastic containment measures but using face masks and social distancing, the percentage of the population that should have passed the disease would be between 28-42%, which is far from the percentage of people that have transited the disease according to the seroprevalence study 13 The proposed model is a classical difference equations system. In constructing the system, we assumed the usual hypothesis of a homogeneous population, whereby any individual of the population is able to infect another. We did not consider the clinical characteristics of the patients different from those of the classification according Table 1 . Population groups in relation to SARS-CoV-2 infection and the evolution of the COVID-19 pandemic, and equations predicting the quantification of each group in each moment in time. 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