NEIGHBOR SCORE: IMPACT OF NEIGHBORING REGIONS IN COVID-19 OUTBREAK

COVID-19 has affected people from all over the globe. This highly contagious disease is spreading from one region to another by people through traveling. The authorities are now trying to identify high-risk and low-risk regions considering each region as isolated. In reality, the regions of a country are connected through buses, trains and, airplanes, etc. and peoples are taking steps to go elsewhere to earn their livelihood. So, preventive and protective measures like lock-down fail to be effective. In this paper, we propose a metric named Neighbor Score to determine the actual invaded scenario of a region considering its adjacent i.e. neighbor regions. As a part of this research, an experiment is conducted with different COVID-19 affected regions of Bangladesh. The experiment has found that the coefficient correlation value of neighboring regions' total COVID-19 cases is positive (0.54 for 50% regions). We have also ranked and zoned the different regions of Bangladesh applying the Neighbor Score.


I. INTRODUCTION
The world is going through the COVID-19 pandemic declared by the World Health Origination (WHO) on March 11 [1]. Corona VIrusDisease 2019 (COVID- 19) was first confirmed at Wuhan in China on December 2019. The reproduction value, of COVID-19 is greater than 2.0 which indicates itself as a highly contagious disease [2], [3]. Till June 22 2020, COVID-19 has infected 8,860,331 people and caused death of 465,740 over more than 215 countries [4]. People are the primary vector of this disease. COVID-19 is spreading at a great speed through people from one country to another for advanced facilities of modern globalization i.e. travel comfortableness and ease connection among countries [5]. On February 2020, many countries impose international travel restriction as an effective action to avoid case importation of COVID-19 from highly infected countries [6]. Alongside, applying lock-down all over the country is a procedure of containment of COVID-19 from further spread of existing cases. But due to the bad impact on the economy, the authorities are applying partially lockdown. The regions in countries are ranked (high-to-low) and zoned (high, intermediate and low-risk zones) [7], [8]. In ranking and zoning, the information of the neighbor region is not considered. As a result, travel availability such as bus, train, etc. for work or other necessary tasks can spread COVID-19 from higher to its adjacent lower infected regions [9]. The information about neighboring regions' can also help us to understand better the situation of a region and take proper action for that region. In this paper, we are proposing a metric naming Neighbor Score to measure a region's COVID-19 situation considering its own and neighboring regions.

II. LITERATURE REVIEW
There are established mathematical models and metrics in the field of infectious disease like COVID- 19. The classic epidemic model is Susceptible-Infected-Removed (SIR) [10], [11]. The entire population is divided into three states: Susceptible(S), Infected (I) and Removed (R). Every individual of population is susceptible by birth for nonvaccine disease like COVID-19. An individual goes from state S to I and then to R with immunity or dead. The popular variant of SIR model applied on COVID-19 is SEIR (Susceptible-Exposed-Infected-Recovered) model.
Here, E refers to a condition that susceptible individual has come contact with infected. R state indicates recovered with immunity. SEIR is applied to assess the effectiveness of measures taken by the authorities [3]. The other popular variants of SIR are MSEIR and SIS [10], [12]. State M refers to temporal immunity through birth of an individual. After end of temporal immunity, that individual becomes susceptible. SIS model (Susceptible-Infected-Susceptible) is applied on disease with no immunity.
The works on spread of epidemic disease on network is recognized [12], [13], [14]. The works have found that spread rate of epidemic depends largely on structure of social network. Construction of contact network compliments the existing models. In contact network , the vertex set is of the people and edge set is of the connection among people. The degree of a vertex refers to occurrence number of that vertex on edge set. The researchers have found that person with higher degree increases the chance of being infected than person with lower degree.
Reproduction number, is the most popular metric for any infectious disease. The basic reproduction number, measures the average number of secondary infections by an infected [10], [15]. A disease with less than 1 will die out but greater than 1 indicating will spread. The higher value of refers to higher spread of disease. The researchers have found that of COVID-19 is higher than SARS [2], [3].The of COVID-19 value varies in different countries because of geographical location, preventive measures, etc. The authorities take actions accordingly for each country like lock-down, partial lock-down, etc. depending on value of that country's . For estimating the reproduction number early in an epidemic, a Bayesian statistical framework is proposed in [16]. Their studies estimate the temporal patterns and were applied during the SARS pandemic for the early monitoring of the effect of control measures. Another metric named contact number, calculates the number of contacts by an infected [10]. determines the number of exposed population. The value of remains low with quarantine, physical or social distancing, etc.
Ranking is used to rank high to low risk regions. Pluchinoet. al. use epidemic data, health-care and environmental information like air pollution, housing information etc. to rank the high-risk cities of Italy [7]. Ren et. al. try to identify high risk regions in China mega-cities using epidemic data [8].
Zoning concept is used to divide different regions of a country into several zones like red, yellow/orange and green by two interval points, and [17], [18]. Zoning is generally applied with total COVID-19 cases of regions, and its function is described below: The principle metric used in ranking and zoning is total COVID-19 cases of a region. Sometimes, is normalized into number of cases per 100,000 people of region. The neighbor regions cases alongside own region's cases can be more practical in ranking and zoning.

III. NEIGHBO R SCO RE
Let there are n number of considered regions and region set, . The adjacent regions are called neighbor. The neighbor set N is the subset of Cartesian product of . The region and neighbor set construct un-directed weighted graph i.e. region network ,

(
) where vertex set is and edge set is . There is an attribute representing total number of COVID-19 cases of region, . The weight function of each neighbor edge to is defined as, There is a transmission function, for all neighbor edges representing the rate at which a COVID-19 case is transmitted from to .
There are two matrices of equal dimension , net weight, and net transmission, . Net weight matrix, compute weight from region, to region, and net transmission matrix compute transmission rate from region to . The shortest-path, p for all-pair regions can be found applying appropriate algorithms.
For the shortest-path from region to , we compute and .

( ) { }
According to (6), as only and is the set of regions with net weight less or equal to 1. Now, we compute neighbor score.

RESEARCH PAPER
Available Online at www.ijarcs.info

A. Data Collection & Experimental Settings
Bangladesh is constituted of sixty four autonomous administrations, named district [21]. The data about districts are collected from website of Bangladesh National Portal [22]. We have considered each district as a region. In this paper, we are experimenting with and . For simplicity, we assume weight of each edge, and transmission rate of each edge, . The regions (i.e. districts) constructed a graph i.e. region network, RN (see Fig. 2.).
is the union set of and its adjacent regions. The degree of a region, in RN is determined by (9).

( ) ∑
The of Bangladesh's region network is 4.25. The regions are plotted in the graph according to their latitudes (yaxis) and longitudes (x-axis). The dates of first confirmed cases of regions are also labeled. To answer the question RQ, we have collected region wise COVID-19 distribution from the daily report of IEDCR [23] dated from April 13, 2020 to May 15, 2020. We explore shortest-path for all pairs of regions. Here, the region network is un-directed equi-weight graph, we apply Breadth First Seacrh (BFS) to find out the shortest paths. Then, we compute net weight matrix, and net transmission matrix, .

B. Experimental Results
The correlation values are plotted in Fig. 3. The lowest value is positive indicating the relationship between a region and its neighboring regions is positive in COVID-19spreading. The correlation values of more than 50% districts are above 0.54. So, research question RQ finds out that there exists relationship among neighboring regions in COVID-19 outbreak. Neighbor Score can be used in ranking and zoning application. These two use total COVID-19 cases of a region, . In those applications, Neighbor Score rather than can produce effective output in infectious disease like COVID-19.Based on data till June 13 2020, regions of Bangladesh are ranked and zoned applying and in Fig. 4. and Fig. 5 (4.25).Chittagong has higher number of cases but its adjacent (i.e. ) regions have lower cases. Munshiganj has highest degree of 7 in region network resulting in placed on top five in both scoring. Dhaka and Narayanganj have higher number of cases individually. Though Tangail is lower-risk region in but take place top five in score due to higher degree and being adjacent of Dhaka. Only one region has crossed the 5000 mark in but there are 10 regions crossed that mark in because of higher average degree (4.25). The regions are colored red, yellow and green according to 'Bangladesh Risk Zone-Based COVID-19 Containment Implementation Strategy/Guide' [18]. In (1), is normalized into number of total cases per 100,000 populations. According to [18], we set and per 100,000 people based on. The three regions are colored red, rest sixty-one regions are yellow and two regions are green in . But 30 regions are red and rest 34 are yellow in . The number of red zones increases significantly. Tangail is one of lower and green region in . But it becomes a red zone in due to higher degree, .

V. CONCLUSION AND FUTURE WORKS
Now, the different regions form a connected region network due to advanced facilities of globalization like bus, train, or air-plane. Due to the high reproduction number of COVID-19, it is spreading from high-risk to adjacent low-risk regions through people. So, the authorities should take measures considering not only own regions but also neighboring regions. Our proposed Neighbor Score metric can capture the situation of a region better and help to take proper measures. In future studies, Neighbor Score will be revised with epidemic (like number of deaths, a number of recoveries, etc.), geographic (like temperature, air quality, etc.), demographic (like gender, age, etc.) and health-care (like a number of hospitals) data of regions.