With each passing day, natural disasters intensify and threaten the safety of people [1-5]. According to the Center for Research on the Epidemiology of Disasters [6], 102 countries had suffered some form of natural disasters by the end of 2016, leaving numerous losses of human lives and heavy economic losses [7-9].

Hydrometeorological events are intensifying, with cyclones being the most destructive phenomenon in the tropics, for all that they bring in their wake: strong winds, sea penetrations, landslides and intense rainfall [3,10-13]. The 2017 hurricane season marked several absolute values, with hurricanes Harvey, Irma, Jose and Katia standing out. Irma reached category 5, even before reaching the Caribbean Sea: also, the one with the longest duration with this intensity [14]. It was, in turn, the most devastating meteor in terms of material damage in the region [6]. It is worth noting that three hurricanes formed in the Atlantic Basin, which does not happen easily. Studies carried out in relation to Climate Change foresee a greater intensity in their formation, which is not far from reality according to what happened in the 2017 cyclonic season [6,14].

A large number of earthquakes occur at the level of planet Earth, and the deaths associated with these phenomena are substantial [14-15], as well as the economic and material damage associated with these phenomena, it is for this reason that it is necessary to forecast these events with the necessary anticipation that allows decisions to be made early enough to save lives and resources [14-16]. There are phenomena in nature that are influenced by the 11-year solar cycle, among them we have, atmospheric pressure, mosquito density, the number of children with acute lymphoid leukemia [17-20], as well as an endless number of climate variables and earthquakes are not alien phenomena to the climate system that is interconnected and interrelated to each other phenomena, if we stick to the philosophy that everything has to do with everything according to geographers, the information to be explained in a model depends on a certain number of variables and as these increase, then the way to explain it truthfully increases.

Forecasting both hurricanes and earthquakes is an arduous task for scientists and of utmost importance to preserve human life [12,21-26]. Some authors have modeled and predicted global earthquakes using the ROR methodology, which consists of several steps [14-15,19,27], and allows not only to mathematically model mosquito larval densities, as well as the population dynamics of mollusks, but goes beyond (possibility of modeling infectious entities of different etiologies, such as HIV/AIDS, Cholera, Influenzas, Acute Respiratory Infections (ARI), Acute Bronchial Asthma Crises (CAAB), Fasciolosis, Angiostrongylosis and even, in the estimation of the length and area of the universe, monthly forecasting of precipitation and extreme temperatures, forecasting of meteorological disturbances/hurricanes, prediction of the latitude and longitude of earthquakes, search for information on white noise, modeling of the equivalent effective temperature (TEE) and atmospheric pressure (PA) up to the electricity consumption of a municipality, province or nation itself [14-15,17-19,28-34].

The objective of the work was to demonstrate how both hurricanes and earthquakes can be predicted by mathematical modeling. 

Description Of The Study Area

The first part of the research was carried out in the municipality of Caibarién, which belongs to the province of Villa Clara, located in the central region of the island of Cuba, (Latitude: 22º 29'40'' N, Longitude: 79º28'30'' W), together with 12 other municipalities that make up the province, from the political and administrative point of view. The municipality of Caibarién is located on the north coast of the province, it has geographical limits with the municipalities of Remedios and Camajuaní.

To carry out the second part of the study, we used a database that was sent in 2013, on July 10 by a student from the University of Paraná, named Wisland. This database is held by the Provincial Meteorological Center (CMP) of Villa Clara, Cuba, and covers from 2000 to 2011. These data could not be updated until 2021, because we did not have access to internet due to COVID-19, but due to the earthquake that occurred in this country on August 14, we decided to run the mathematical models for forecasting these phenomena and to have a guide for the future management of these events in Haiti.

We took into account the 11 year cycle, which influences many natural phenomena, such as population densities of mosquitoes, children with acute lymphoid leukemia, as well as hurricanes, among others: Hence, we first modeled the year in which earthquakes of magnitude 6 or more should occur using a short-term parameter, then we added 11 steps backwards, 11 of the solar cycle that influences the forecast of total earthquakes at a global level, until the year 2096, we forecast the latitude, longitude as well as the month, day, hour, magnitude and depth for earthquakes of magnitude 6 or more with the ROR methodology. 

Objective Regressive Regression (ORR) Methodology

In the methodology of the Regressive Objective Regression ROR, dichotomous variables DS (Sawtooth), DI (Inverted Sawtooth) and NoC (Trend) are created in a first step, where:

• NoC: Number of base cases

• DS = 1, if NoC is odd: DI = 0, if NoC is even, when DI = 1, DS = 0 and vice versa

Subsequently, the module corresponding to the Regression analysis of the statistical package SPSS, version 19.0 (IBM) was executed, specifically the ENTER method, where the predicted variable and the ERROR are obtained.

Then the autocorrelations of the variable ERROR were obtained, paying attention to the maximums of the significant partial autocorrelations PACF. The new variables were then calculated taking into account the significant lag (Lag) of the PACF. Finally, these regressed variables were included in the new regression in a process of successive approximations until obtaining white noise [35] in the regression errors. For the case of atmospheric pressure, lags of 1 year in advance were used, although with 11 years’ good results are obtained [14-15,19,27].

It was possible to forecast the atmospheric pressure variable one year in advance, as can be seen in Figure 1: an extreme weather event was to occur between days 12 and 13, due to the large pressure drop that was expected according to the ROR modeling [19,29-30].

What actually happened can be seen in Figure 2, where the pressure drops from Hurricane Irma occurred approximately three days earlier than predicted, but the coincidence of the data was astounding.

Figure 1: Three-Hourly Atmospheric Pressure at Station Level in Caibarién

Legend: Unstandardized Predicted Value. Pm: Trihourly Atmospheric Pressure

Figure 2: Pressure during Hurricane Irma in September 2017

Caibarién Station. PRE_2: Tri-Hourly Pressure Predicted One Year in Advance According To ROR. Pe.: Tri-Hourly Pressure Occurred in the Month of September 2017. Caibarién Station. X Axis: Number of Observations. Y Axis: Atmospheric Pressure in Hectopascals (Hpa)

Figure 3: Crosscorrelation (CCF) Between PRE_2 and Pe in Caibarién, Cuba. September 2017

When studying the crosscorrelation in the small, it could be seen that in lag 3 it showed a high significant coefficient, indicating the close relationship between the forecast and the actual value Figure 3.

The strong and increasingly frequent and unusual summers and winters, floods, droughts, meteorological disturbances (gales, tropical storms, cyclones, hurricanes, among others), reinforced by the sporadic intervention of "El Niño and La Niña" and more worryingly, the inconsequential participation of man, as well as the increasing increase of air and maritime transport, are worryingly perpetuating these and other epidemiological episodes [9,36-39]. Therefore, it is undeniable that meteorological variables have a much more marked influence on vector organism populations, and transmissible entities [28,30,40].

Figure 4: Actual and Unstandardized Predicted Value according to ROR

The above analyzed has a direct impact on the species of vector organisms transmitting infectious entities [17,29-30], to which is added climate change, with its more than 20 natural phenomena, directly responsible for the increasing spread and presentation in different tropical and subtropical regions of infectious entities of viral and parasitic etiology [41-43], as well as the spread, irradiation and propagation of different vector genera and species, mainly Anopheles, Culex, Aedes aegypti and Ae. Albopictus Skuse 1895, which is consistent with results predicted by other authors [17,32,43-44].

If we take into account all of the above, plus the results obtained in articles published in relation to the subject under analysis [32,45-46], since it is to be expected, in the very near future, transient/temporary ecological shifts/shifts for culicid species from coastal ecosystems to urban ecosystems/settlements, even more than 50 km away from the coasts, with the consequent epidemiological consequences that this phenomenon could bring with it, both for human health and for the rest of the animals: i.e. focal explosions of zoonotic entities in areas/sites that do not coincide with the ecology and biology of vector species and intermediate hosts.

Mathematical Modeling for Earthquakes in Haiti

The model for the year in which earthquakes of magnitude 6 or more should occur, 100% variance is explained with an error of 0.56 Table 1.

Figure 4 shows the forecast for the year and shows its increase according to the global trend of earthquakes, which is increasing [15,27].

As we do not have the latitude and longitude data for the earthquake of August 14 in Haiti, since we do not have Internet access due to COVID-19, we will focus on the next earthquake, which should occur in the year 2031, according to the forecast for all parameters Tables 2 and 3, these values are in red.

Table 1: Summarized Model According to the Year in Which Earthquakes of Magnitude 6 or More Should Occur

A: Predictores: Unstandardized Predicted Value b: For regression through the origin (the model without intercept), R-squared measures the proportion of the variability in the dependent variable about the origin explained by the regression. This CANNOT be compared to R-squared for models that include intercept. C: Dependent variable: Year d: Linear regression through the origin

Table 2: Summary Of Cases for the Variables: Year, Month, Day, Hour and Minute According to the Forecast for the Next Earthquake in Haiti

A. Limited to the First 100 Cases

Table 3: Summary Of Cases for the Variables: Year, Latitude, Longitude, Depth and Magnitude According to the Forecast for The Next Earthquake in Haiti

Table 3: Continue

A: Limited to the First 100 Cases

It was shown that the forecast coincided with what happened during the passage of Hurricane Irma, where the prediction of the tri-hourly atmospheric pressure one year in advance is an important tool for forecasting the impact of hurricanes in our territory, as well as its direct relationship with the appearance and spread in different tropical and subtropical regions of infectious entities, both of viral and parasitic etiology, and of different genera and species of vector organisms. In addition, it was shown that the trend of earthquakes is increasing on a global scale, and that they can be predicted by the 11-year solar cycle, as will happen in Haiti in 2031.

Acknowledgements

We thank the Department of the Group of Instruments and Methods of Observation (GIMO) of the Provincial Meteorological Center of Villa Clara for the data provided.

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