A Critical Analysis of the Hospitalization Network for COVID-19 Patients in Bahia, Brazil in the first wave of the pandemic

To effectively combat the COVID-19 pandemic, the state government of Bahia, Brazil, 1 has distributed intensive and non-intensive care units along the nine regions that divide the state 2 of Bahia, such that COVID-19 patients could be easily hospitalized in health care units located at 3 the same regions where they live. However, the observed hospitalizations networks for COVID-19 4 patients shows that a considerable number of COVID-19 patients had to travel beyond their region 5 of residence to be hospitalized. Hence, this study indicates that the current distribution of health 6 care units in Bahia, Brazil, is not sufficient to effectively reduce the distances traveled by COVID-19 7 patients requiring hospitalization. We believe that such unnecessary travels to distant hospitals may 8 put the sick patients as well as healthy people involved in the transportation process in risk, further 9 delaying the stabilization of the COVID-19 pandemic in each region of the state of Bahia. 10


Introduction
The state of Bahia, Brazil, has a total area of approximately 565,000 square kilometers 13 and, by the end of 2020, an estimated population of about 15 million people, which is 14 superior to the estimated population of European countries, such as Belgium, Greece, 15 Sweden, and Portugal [1]. In this sense, while in normal conditions, it is already difficult 16 to provide free, high-quality health care services to the population that live in Bahia, 17 in March 11, 2020, with the World Health Organization (WHO) announcement of the 18 coronavirus disease 2019  outbreak, caused by the new severe acute respiratory 19 syndrome coronavirus 2 (SARS-CoV-2), as a pandemic, the provision of high-quality health 20 care services has become even more challenging, since the high transmissibility of the 21 SARS-CoV-2 may quickly overload health care services of a state or a country [2]. 22 Possibly inspired by the National Health Service of the United Kingdom [3], the 23 Brazilian National Health System (Sistema Único de Saúde -SUS) is a public health system 24 created by the Constitution of the Federative Republic of Brazil [4]. In the state of Bahia, 25 Brazil, the management of SUS is done by the state government of Bahia, that must 26 provide financial resources and stimulate the municipalities of Bahia to pursue a responsible 27 management of their health care services, and that must also assume that responsibility in 28 the case some of those municipalities are not able to achieve that goal [5]. 29 By the end of October 2020, following the State Contingency Plan for Confrontation 30 of the New Coronavirus SARS-CoV-2 [6], the state government of Bahia distributed 2,286 31 intensive and non-intensive care units in 61 out of the 417 municipalities of Bahia, in order 32 to provide better assistance to the COVID-19 patients that live in Bahia [7], 41% higher 33 than the previous healthcare network. Many of these health rooms were created to serve 34 COVID-19 patients, as part of a municipal, state, and federal effort. Therefore, COVID-19 35 patients that reside in municipalities not capable of providing appropriate treatment or 36 hospitalization for such a disease, must travel to another municipality to be better assisted 37 by SUS. In order to reduce the distance and duration of those travels, the state government 38 of Bahia has distributed health care units into municipalities located into nine regions 39 (i.e., North, Northeast, North-Central, East-Central, East, West, Southwest, South, and 40 Extreme-South) that geographically divide the state of Bahia, such that COVID-19 patients 41 could be ideally treated or hospitalized in health care units available at the regions where 42 they reside, promoting a region-based control of the COVID-19 pandemic inside the state 43 of Bahia.

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Related work has already shown that we need to analyze transportation networks be-45 tween municipalities and states of a country [8] [9][10] [11] to be able to study the dynamics 46 of dissemination of infectious diseases, such as COVID-19 [12] [20][21] of Bahia. 49 In this paper, we aim to evaluate whether the distribution of intensive and non-50 intensive care units among 61 out of the 417 municipalities in Bahia is enough to assist 51 COVID-19 patients inside each one of the nine distinct regions that divide the state of Bahia. 52 On the basis of a dataset provided by the Health Secretary of the State of Bahia (Secretária de 53 Saúde do Estado da Bahia -SESAB) and by the Brazilian Ministry of Health (Ministério da 54 Saúde do Brasil), from open health systems data, we have built a hospitalizations network 55 for COVID-19 patients in Bahia, Brazil, based on the concepts of complex networks and 56 using geoprocessing. Then, we have analyzed whether COVID-19 patients are indeed 57 being hospitalized in health care units located in the same region where they live, and if 58 that is not the case, what is the relation of importation and exportation of hospitalized 59 COVID-19 patients between distinct regions in Bahia. Another contribution of our work is 60 the presentation of the DESH (Degree of External Search for Hospitalization) index, which 61 estimates the saturation level of the municipalities that offer in-hospital assistance for 62 COVID-19 patients that come from other regions of the state of Bahia. We believe that the 63 discussions presented in this paper may be helpful to the state government of Bahia, which 64 may improve its decision-making process to effectively control the COVID-19 pandemic in 65 Bahia, and we also believe that this kind of study may be replicated for other states and 66 countries around the world, to verify whether the hospitalizations networks previously 67 estimated by governments match the real ones obtained in practice. In this study, we considered the COVID-19 patients that were hospitalized in intensive 71 or non-intensive care units provided by SUS in the state of Bahia, Brazil between March 1, 72 2020 and July 30, 2020, and that have been reported in the hospital systems. To build the 73 hospitalizations networks, we included 4,387 COVID-19 patients that were hospitalized in 74 municipalities distinct to the ones where they were residents at the time of the diagnosis, 75 with the goal of identifying whether those patients had to travel large distances to be 76 hospitalized due to the unavailability of health care units in their municipality of residence. 77

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On the basis of the graph theory, we represent the hospitalizations networks for 79 COVID-19 patients in Bahia as a directed graph, where each node is assigned to a munici-80 pality in Bahia, each node's size is directly proportional to its DESH index to be presented 81 in the next subsection, each directed edge represents a travel going from an origin (i.e., 82 municipality of residence) to a destination (i.e., municipality of hospitalization), and each 83 directed edge is weighted by the number of patients that traveled between the correspond-84 ing pair of origin-destination municipalities. Hence, the hospitalizations networks provides 85 a visual representation of the patients that needed to be hospitalized because of the severity 86 of COVID-19, but could not be hospitalized in their municipality of residence due to the 87 unavailability of a health care unit at that location and at that moment. In order to evaluate whether the strategy of the state government of Bahia to distribute 90 health care units among the nine regions in Bahia has been successful, we simulated 91 the expected hospitalizations networks idealized by the state government. To do so, 92 we redirected each edge of the observed hospitalizations networks to connect the node 93 representing the municipality of residence of the patient to another node representing the 94 closest municipality with an available health care unit, such that each redirected edge could 95 represent the expected path traveled by a patient when searching for hospitalization by 96 COVID-19 in Bahia. To favor a comparison between the level of assistance and hospitalization provided by 99 each region of the state of Bahia, we have developed the DESH index. With such an index, 100 we can measure the saturation level of the 61 municipalities able to hospitalize COVID-19 101 patients. While each one of those 61 municipalities must provide assistance to the internal 102 demand for hospitalization, by providing support to the patients that live inside the 103 corresponding municipality, the DESH index only takes into account the external demand 104 for hospitalization. In other words, this index measures how much each municipality is 105 involved in the importation of COVID-19 patients provided by other municipalities that 106 could be located inside or outside of the corresponding region of the state of Bahia.

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The DESH index of a municipality i, or node i, with at least one intensive or non-108 intensive care unit available, can be described in terms of the following Equation 1: 109 This is the example 2 of equation: , where wij is the weight of a directed edge that connects the node i to the node j (i.e., 111 number of patients that traveled from municipality j to municipality i), i is the total number 112 Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 9 February 2022 doi:10.20944/preprints202202.0137.v1 of intensive and non-intensive care units available at that municipality i, and N is the total 113 number of municipalities being evaluated. Each one of the nine regions of Bahia is represented by a specific color. Each node (red 115 circle) of the directed graph represents a municipality of Bahia. Each node size is directly 116 proportional to its DESH index. The weight of each directed edge (black line) is directly 117 proportional to the number of patients that have been transported to the corresponding 118 municipality for hospitalization.

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As we can see in Figure 1a, according to the original planning of the state government 121 of Bahia, even if not every one of the 417 municipalities of Bahia has a reference hospital or 122 health care unit able to treat COVID-19 patients, the expected hospitalizations networks 123 for COVID-19 patients would be the one in which each patient would be hospitalized in 124 the nearest reference unit available in the region where the patient is residing, such that 125 COVID-19 patients would travel a distance as minimum as possible to be hospitalized, 126 consequently allowing for a faster and more efficient treatment of those patients, as well as 127 for a lower exposition to the COVID-19 of the professionals involved in the transportation 128 process. Hence, as can be seen by the weights of the directed edges shown in Figure 1a, 129 once the health care units of each region would concentrate the hospitalization cases of 130 the patients that live in the corresponding municipalities, the hospitalizations networks 131 would be more distributed all over the state, and the COVID-19 pandemic could be handled 132 locally, per region of the state of Bahia. However, on the basis of the anonymized data 133 collected from SESAB, we could estimate that the observed hospitalizations networks for 134 hospitalized patients are more similar to the one illustrated in Figure 1b. In this case, we 135 can see that several COVID-19 patients need to travel from one region to another to be 136 properly hospitalized, which suggests that some regions of the state of Bahia are not able to 137 handle the high demands of hospitalization that may be happening due to COVID-19. In an 138 ideal, expected scenario depicted in Figure 1a, each region would hospitalize only resident 139 patients diagnosed with COVID-19. However, Table 1 shows that, while both North, East, 140 and Southwest regions exported a few patients to the other regions of the state of Bahia, 141 North-Central, East-Central, and Northwest regions exported more than three times the 142 number of patients that they could hospitalize. We can also observe that both East and 143 Southwest regions concentrate the highest percentage of imported hospitalizations. In this 144 case, it is worthy to note that almost 50% of the hospitalizations done in the East region, 145 that includes the capital of the state of Bahia, Salvador, are imported from other regions, 146 while only 0.5% of the hospitalized cases are exported to other regions.

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One of the main problems caused by such an unbalanced observed hospitalizations 149 networks is illustrated in Figure 2, which shows that, while in the expected hospitalizations 150 networks, some travels would be required to transport patients between the municipalities 151 of the same region, in the observed scenario, more patients needed to travel longer distances 152 to be hospitalized outside of their region of residence. In our point of view, that unnecessary transportation of patients may affect the state 154 of Bahia in two ways: First, this scenario may reduce the effectiveness in the reduction of 155 the number of new cases of COVID-19 per region of the state of Bahia, since new patients 156 diagnosed with COVID-19 might end up being hospitalized in another region that has 157 already stabilized the COVID-19 pandemic, exposing healthcare professionals of such a 158 region to the coronavirus, that, once infected by COVID-19, could further disseminate 159 such an infectious disease to other people, contributing to a new rise in the number of 160 new cases of COVID-19 per day. Second, that unnecessary transportation may result in 161 additional costs for the state and the municipalities of Bahia, since they both are financially 162 responsible for the management of the healthcare professionals and the infrastructure 163 required to realize the transportation of the patients to be hospitalized, and also for the 164 maintenance of the intensive and non-intensive care units that otherwise would be empty 165 or at least less occupied, assuming a scenario in which a region is exporting new COVID-19 166 patients to be hospitalized in another region that has achieved stabilization with a few new 167 cases of COVID-19. 168 In Figures 3, 4, 5 e 6, we show a more detailed visualization of the observed hospital-169 izations networks previously shown in Figure 1b

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COVID-19 is a dangerous infectious disease that requires new policies of the govern-186 ments in order to effectively combat the further prolongation of this pandemic. In this 187 sense, the provision and distribution of new hospitals and health care units able to assist 188 and hospitalize COVID-19 patients is desirable to allow for a faster and more effective 189 treatment of those patients.

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As we have shown in this paper, the distribution of intensive and non-intensive care 191 units in the state of Bahia, Brazil, has some limitations, since many patients had to travel 192 more than 300 kilometers to be hospitalized, as shown in Figure 2. Hence, a redistribution 193 of the available health care units, or alternatively a selective, adaptive expansion of the 194 health care infrastructure in the regions that are exporting most of their patients to be 195 hospitalized in another region, may contribute to a more successful reduction in the length 196 of these travels.