January 16, 2021

# "Mathematics to look for disappeared"

How fast does a four-year-old boy walk? and one of seven? Does a person older than 70 travel the same distance as a younger one but with dementia? It is these and many other data that are analyzed in the search for missing persons. Today the Day of the Disappeared is celebrated without apparent cause. Only since 2010, 176,063 complaints have been filed for this reason. Of these, 12,330 are still active, according to the Ministry of the Interior. Searches to which the thousands of cases prior to that date should be added. In addition, in many cases people were found already without life.

Despite this, «Spain has not yet implemented the international methodology used in countries such as the United States, Canada, the United Kingdom or New Zealand throughout the country», explains José Vicente Romero, Navarre firefighter and head of the section of Navarre of SOS Disappeared.

In order to increase the probability of success, two and a half years ago this expert and Manuel Jabalera, of the Emergencies Group of Andalusia (GREA), with the collaboration of writer and researcher Robert J. Koester, began to translate manuals and analyze statistics to try to refine the search as much as possible.

"It is necessary to use statistics to have a better chance of finding a missing person alive because there is not enough staff to be able to comb everything. With this international method – '' Manual of Search and Land Rescue '' -, we can reduce the search area by up to 90%, which increases the probability of success", it states.

The use of mathematics is basic. "When a person disappears," he continues, "four methods are combined whose data must be crossed to refine the search: the theoretical, the statistical, the subjective and the deductive, in that order." The first one allows us to know the probable search zone, "taking into account the speed for time since that disappeared in order to calculate the distance traveled. The problem is that it fails a lot to perform this calculation ». After which we proceed to the statistical method in order to achieve a lower search radius. "The first thing that is done is to investigate the environment of the disappeared person to have an exhaustive profile of that person and to try to know what could have happened. It is also essential to protect the Initial Planning Point (PPI) in case it was not a voluntary disappearance and we had to investigate traces.

«This statistic is the one that allows us to know that with a 95% probability a child of one to three years will travel 4.5 km of horizontal distance in a rural environment; that one of three to five will walk 21.4 km of radius in a straight line or that a person with dementia will travel 8.3 km ».

It is about "playing" with statistics, with results thrown by thousands of previous cases. Thus, it can be detailed that, "with a 25% probability, the person with dementia will travel 300 meters, with a 50% probability of 800 meters and with 75%: 1.9 km. From these data, we must analyze the distance to beat, use the statistics to have a better chance of finding that person, decide whether to work with a 25% probability or 50% according to the statistics (the type of person according to the 42 categories) ».

Romero points out that this progress must also be stopped, preventing them from reaching cliffs, passing through customs, etc. In addition, the displacement corridors are focused because statistically 50% of the disappeared are located on routes, roads, streams, railways. At the same time, high probability tasks are analyzed, ie those decision points of attraction, for example in a person who has a high risk of suicide, it is very frequent that he chooses to go to very visual sites such as a viewpoint. The decision points are also taken into account, those crosses in which the person will have to make the decision, whether voluntary or not, to go one way or the other ». In this case one can think that the fact of being left-handed or right-handed can change the direction, but "the statistics tell us that the taking of one direction or another is not significant".

With the subjective method areas are eliminated where it is very likely that it is not, for example that could not go through having a deep river. "In this case the river would be analyzed in case it was there but it will not go beyond the river." The same thing that would happen with a highway. The next method is the deductive, putting everything else together to further limit the search area. "For example, they denounce that five years ago a person with dementia disappeared, that would give us, according to the theoretical method, a radius of 20 km (an area of ​​1,256 km2), after which the rest of the rings would be made. Thus, according to the statistical method, the radius would be 8.3 km; that is, an area of ​​216 km2, so we have removed more than 1,000 km2 ».

Despite the different training courses given in this regard, «In Spain this usual international method has not yet been implemented in other countries, due to the language barrier». We are not the only ones, "Chile has been interested in our manual, which is free, which is why they have obtained statistics that otherwise would not have been possible, thus allowing to unify in a single manual, hundreds of international publications."

«It is a year-long job, generous and free, that only has one condition that this work can not be charged», as highlighted by Joaquín Amills, president of SOS Desaparecidos. All with a goal, improve searches. However, despite everything that mathematics can help, there will always be cases that will not adjust to the usual case.

.