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urgent matter. Reports of migrants threatened by smugglers, forcibly held by police or killed by criminals were
rare in the past but have been increasingly heard in the last few years. This rise appears to have coincided
with the growth in trafficking and smuggling , so too the wider use of guns.The increased instability on the
way to haven countries make many migrants panicked and threatened. On the other side, the war condition in
migratory place also contributes to this index. To propose a safety index becomes crucial.And the measurement
of this index defined as S
t
ij
(from place i to place j) is calculated by our model in the following.
• Environmental acceptance
The environmental acceptance C
ij
is undoubtedly significant as refugees whom we assume to be sensible will
compare the environment of the destination with that of the origin district i. Here, the environment acceptance
is not merely referred to living environment or maximum capacity in country j but also include three main
factors:
(1) Resource Abundance. Food supply and water availability is the basis of living. Besides,access to primary
health-care, referral systems, specialized health services, psychosocial-medical units and child health support
are all in need to cope with wound and trauma in a desired destination.
(2) Economic condition. The economic development level also determines whether the migrants can sur-
vive on.Education and communications systems, commercial installations are needed for the functioning of a
community. Many indicators such as social well-being of people, job opportunity and so on are considered. As
economist Amartya Sen points out, ”economic growth is one aspect of the process of economic development.”
In our model, we take GDP as the main indicator of economic condition.
(3) Religious and culture acceptance. Different communities have varied beliefs, which may lead to mis-
understandings, conflicts and discrimination. Whether a culture is inclusive plays a role. In addition, as official
languages, customs, ceremonies etc. vary from place to place, which might be a burden for communication
between migrants and local people, thus cultural acceptance
Migration groups especially vulnerable ones, like children, unaccompanied and separated minors, pregnant and
lactating mothers, the elderly, disabled and people look for a place of environmental acceptance, which has
been limited due to the desire by refugees and migrants to continue on with their journey and an unwillingness
to remain in unrest.
• Transportation index
To transport from place i to place j, one needs to balance a comprehensive transportation cost with regard
of time, distance and traffic condition related to the type of transportation etc..Thus a transportation index
Conv
i
is defined.
• Ratio of repatriation in period T
The quantity of refugees who get granted is limited in an entry point, thus the proportion of repatriates or
rejectees are relatively too high, then refugees are less likely to take on a routine head for that node. Therefore,
we also give a notation of B
t
representing the ratio of repatriation in a certain period T in order to better
solve the refugee crisis problem.
• Quantity of nodes
We premise that the quantity of refugees allowed to pass through an entry point is a constant, in this way, the
total number of people who get granted is determined by the number of entry points (node in model). P oint
j
i
is the i
th
entry point in place j. Evidently, the larger the number i, the larger pass probability will be for a
certain group, which affects the choice of refugees.
Taking all those parameters and measures into account, we can step further to define a set of notations in designing
a mathematical model.
3 Notations and Descriptions
Table 1.Notations and Descriptions we define in our model