Mathematical Modeling and Its Applicability from Natural Disasters to Human Health

Abstract

Earthquakes and cyclones are two of the most destructive natural events, with the greatest consequences for both vector organism populations and human health. The objective of the research was to demonstrate how hurricanes and earthquakes can be
predicted by mathematical modeling. The study was carried out based on the forecast of the atmospheric pressure variable, with a series of data, from 1977 to 2016 (tropical cyclones), while, in the case of earthquakes, we relied on the data series of Haiti (magnitude 6 or more), and which have occurred in this country (2000 to 2011), and thus achieve a forecast until the year 2096. The methodology used in the research was the Regressive Objective Regression (ROR). It was shown that the forecast coincided with what occurred during the passage of Hurricane Irma, except for a difference of three days and six hours. Good models were obtained for both longitude and latitude, as well as for month, day, hour, magnitude and depth for earthquakes of magnitude 6 or more. In Haiti it should be similar to the way it is presented in the rest of the world. It was possible to predict the occurrence of earthquakes in that country up to the year 2096. It is concluded that the prediction one and 11 years in advance of the trihourly atmospheric pressure is an important tool to foresee the impact of hurricanes in Cuba, as well as its direct relation with the diffusion and presentation of infectious entities of viral and parasitic etiology. In relation to earthquakes, it is possible to use the 11-year solar cycle to predict earthquakes, and the next one should occur in Haiti in the year 2031, month July, day 14, hour 9.20, minute 25.1, Latitude 36.60, Longitude 133.00, Depth 71.14, Magnitude 6.7 on the Richter scale.

Full text

Scientific Research Journal of Medical Sciences
Abbreviated Key Title: Sci Res Jr Med Sci
ISSN 2788-9475 (Print)
ISSN 2788-9483 (Online)
Volume-2 | Issue-2 |Mar-Apr-2022 |
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Article History
Received: 30.03.2022
Accepted: 05.04.2022
Published: 10.04.2022
32
DOI: 10.47310srjms.2022.v02i02.005
Research Article
Mathematical Modeling and Its Applicability from Natural Disasters to
Human Health
Ricardo Osés Rodríguez1, Rigoberto Fimia-Duarte*2, David del Valle Laveaga3, Meylin Otero Martin1, Nancy
Ruiz Cabrera1, Yanira Zaita Ferrer2, José Iannacone4 and Frank M. Wilford González5
1Provincial Meteorological Center of Villa Clara, Cuba
2Faculty of Health Technology and Nursing (FTSE), University of Medical Sciences of Villa Clara (UCM-VC), Cuba
3Academic Area of Health, Maya World University, México
4Laboratory of Animal Ecology and Biodiversity (LEBA). Faculty of Natural Sciences and Mathematics (FCNNM).
Environmental Sustainability Research Group (GISA). University Graduate School (EUPG). Federico Villarreal
National University (UNFV). Lima, Peru and Parasitology Laboratory. Faculty of Biological Sciences. Ricardo Palma
University (URP). Lima, Peru.
5Center for Bioactive Chemicals (CBQ), Central University "Marta Abreu" of Las Villas. Villa Clara, Cuba
*Corresponding Author
RIGOBERTO FIMIA-DUARTE
Abstract: Earthquakes and cyclones are two of the most destructive natural events, with the greatest consequences for both vector
organism populations and human health. The objective of the research was to demonstrate how hurricanes and earthquakes can be
predicted by mathematical modeling. The study was carried out based on the forecast of the atmospheric pressure variable, with a
series of data, from 1977 to 2016 (tropical cyclones), while, in the case of earthquakes, we relied on the data series of Haiti (magnitude
6 or more), and which have occurred in this country (2000 to 2011), and thus achieve a forecast until the year 2096. The methodology
used in the research was the Regressive Objective Regression (ROR). It was shown that the forecast coincided with what occurred
during the passage of Hurricane Irma, except for a difference of three days and six hours. Good models were obtained for both
longitude and latitude, as well as for month, day, hour, magnitude and depth for earthquakes of magnitude 6 or more. In Haiti it should
be similar to the way it is presented in the rest of the world. It was possible to predict the occurrence of earthquakes in that country up
to the year 2096. It is concluded that the prediction one and 11 years in advance of the trihourly atmospheric pressure is an important
tool to foresee the impact of hurricanes in Cuba, as well as its direct relation with the diffusion and presentation of infectious entities
of viral and parasitic etiology. In relation to earthquakes, it is possible to use the 11-year solar cycle to predict earthquakes, and the
next one should occur in Haiti in the year 2031, month July, day 14, hour 9.20, minute 25.1, Latitude 36.60, Longitude 133.00, Depth
71.14, Magnitude 6.7 on the Richter scale.
Keywords: Solar cycle, infectious entities, Haiti, hurricane Irma, trihourly atmospheric pressure, forecast, Objective Regressive
Regression, earthquakes, Villa Clara.
1.INTRODUCTION
With each passing day, natural disasters intensify
and threaten the safety of people (Zhang and
Krishnamurti, 1999; Socarrás, 2006; Gore, 2007; Dodla
et al., 2011; Cepero, 2012). According to the Center for
Research on the Epidemiology of Disasters (CRED,
2017), 102 countries had suffered some form of natural
disasters by the end of 2016, leaving numerous loss of
human lives and heavy economic losses (Camargo et
al., 2007; Osés et al., 2012; Arnell and Gosling, 2016).
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
(Aberson et al., 1998; Goerss, 2000; Gore, 2007;
Vecchi et al., 2014; Ruan and Wu, 2018). 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 (Osés et al., 2018a). It was, in turn,

Ricardo Osés Rodríguez et al., Sci Res Jr Med Sci; Vol-2, Iss-2 (Mar-Apr, 2022): 32-40
33
the most devastating meteor in terms of material
damage in the region (CRED, 2017). 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 (CRED,
2017; Osés et al., 2018a).
A large number of earthquakes occur at the level of
planet Earth, and the deaths associated with these
phenomena are substantial (Osés et al., 2018a, c), 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 (Osés et al., 2018a,
c; Osés et al., 2021). 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
(Fimia et al., 2017c; Sánchez et al., 2017; Osés et al.,
2017; Osés et al., 2018d), 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 (Wu et al., 2000; Emanuel, 2005;
Webster et al., 2005; Wang et al., 2007; Halperin et al.,
2013; Vecchi et al., 2014; Li et al., 2016). Some
authors have modeled and predicted global earthquakes
using the ROR methodology, which consists of several
steps (Osés et al., 2014; Osés et al., 2017; Osés et al.,
2018a,c), 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 (Fimia et al., 2012; Fimia et al.,
2016a,b; Fimia et al., 2017a,b,c; Osés et al., 2017;
Sánchez et al., 2017; Osés et al., 2018a,b,c; Osés et al.,
2019).
The objective of the work was to demonstrate how
both hurricanes and earthquakes can be predicted by
mathematical modeling.
2. METHODS
2.1 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.
2.2 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.

Ricardo Osés Rodríguez et al., Sci Res Jr Med Sci; Vol-2, Iss-2 (Mar-Apr, 2022): 32-40
34
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 (Jimenez, 2017) 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 (Osés et al., 2014; Osés et al.,
2017; Osés et al., 2018a, c).
3. RESULTS AND DISCUSSIONS
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 (Fimia et al., 2016a;
Fimia et al., 2017a; Osés et al., 2017).
Figure 1: Three-hourly atmospheric pressure at station level in Caibarién
Legend: Unstandardized Predicted Value. Pm: Trihourly Atmospheric Pressure
What actually happened can be seen in figure 2,
where the pressure drop from Hurricane Irma occurred approximately three days earlier than predicted, but the
coincidence of the data was astounding.

Ricardo Osés Rodríguez et al., Sci Res Jr Med Sci; Vol-2, Iss-2 (Mar-Apr, 2022): 32-40
35
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).
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).
Figure 3: Crosscorrelation (CCF) between PRE_2 and Pe in Caibarién, Cuba. September 2017
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

Ricardo Osés Rodríguez et al., Sci Res Jr Med Sci; Vol-2, Iss-2 (Mar-Apr, 2022): 32-40
36
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 (Xie et al., 2006; Ballester et
al., 2010; Arenas and Carvajal, 2012; Roy and
Kovordányi, 2012; Arnell and Gosling, 2016).
Therefore, it is undeniable that meteorological variables
have a much more marked influence on vector organism
populations, and transmissible entities (Fimia et al.,
2012; Osés et al., 2015; Fimia et al., 2016b).
The above analyzed has a direct impact on the
species of vector organisms transmitting infectious
entities (Fimia et al., 2016a,b; Fimia et al., 2017c), 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 (Trenberth, 2005; Kundzewicz et
al., 2013; Zhang, 2015), as well as the spread,
irradiation and propagation of different vector genera
and species, mainly Anopheles, Culex, Aedes aegypti
(Linnaeus, 1762) and Ae. Albopictus Skuse 1895, which
is consistent with results predicted by other authors
(Beck-Johnson et al., 2013; Zhang, 2015; Fimia et al.,
2017b, c).
If we take into account all of the above, plus the
results obtained in articles published in relation to the
subject under analysis (Osés et al., 2016; Aldaz et al.,
2017; Fimia et al., 2017b), 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.
3.1 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).
Table 1: Summarized model according to the year in which earthquakes of magnitude 6 or more should occur.
Model summary c,d
Model
R
R squaredb
Adjusted R-
squared
Standard error of
estimation
1
1.000a
1.000
1.000
.556
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
Figure 4 shows the forecast for the year and shows its increase according to the global trend of earthquakes, which
is increasing (Osés et al., 2014; Osés et al., 2018c).
Figure 4: Actual and Unstandardized Predicted Value according to ROR

Ricardo Osés Rodríguez et al., Sci Res Jr Med Sci; Vol-2, Iss-2 (Mar-Apr, 2022): 32-40
37
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 2: Summary of cases for the variables: year, month, day, hour and minute according to the forecast for the next
earthquake in Haiti
Resúmenes de casosa
Year
Predicted Value
Month
Predicted Value
Dey
Predicted Value
Hour
Predicted Value
Minute Predicted Value
1
2002.13197
.
.
.
.
2
2002.39475
.
.
.
.
3
2002.63362
.
.
.
.
4
2002.89641
.
.
.
.
5
2003.13528
.
.
.
.
6
2003.39807
.
.
.
.
7
2003.63695
.
.
.
.
8
2003.89974
.
.
.
.
9
2004.13863
.
.
.
.
10
2004.40144
.
.
.
.
11
2004.64036
.
14.18248
10.04511
.
12
2004.90322
.
14.02268
9.02375
.
13
2005.14221
.
15.81242
12.80756
34.56724
14
2005.40519
.
12.74509
9.02375
25.32466
15
2005.64437
.
16.42079
9.49261
32.56231
16
2005.90766
6.85723
14.53220
11.04956
27.12909
17
2006.14734
7.76973
14.51455
11.15009
36.97315
18
2006.41145
6.96106
12.78312
9.94457
22.11678
19
2006.65245
7.25058
14.73002
13.54422
36.87291
20
2006.91869
6.85723
14.33448
8.83959
22.01653
21
2007.16315
7.76973
16.59571
12.62340
34.66749
22
2007.43498
6.96106
13.13548
9.94457
22.11678
23
2007.68849
7.35441
16.10394
9.49261
34.36675
24
2007.97494
6.96106
14.60825
8.65543
26.22688
25
2008.25213
7.25058
15.92650
9.67678
32.26158
26
2008.57689
6.75340
14.43081
9.39208
24.32219
27
2008.91606
7.04291
15.90622
13.17589
32.96330
28
2009.34112
7.58405
13.23181
9.76041
23.31973
29
2009.84257
7.56207
15.80736
12.99173
33.76527
30
2010.53020
7.06489
15.17608
7.36628
26.42737
31
2011.45650
7.25058
16.33716
9.49261
37.47439
32
2012.83156
6.75340
13.89849
10.31290
23.62047
33
2014.87013
7.04291
16.23830
13.54422
36.27143
34
2018.04489
7.37639
15.29268
10.12874
23.21949
35
2022.99545
7.97739
16.21802
9.30845
33.26404
36
2030.88189
7.16873
14.32943
9.20792
25.12417
37
2043.45610
7.76973
16.27633
12.99173
35.56970
38
2063.67788
7.27256
14.70206
11.41788
22.21702
39
2096.21109
7.56207
16.96329
9.30845
36.87291
Total
N
39
24
29
29
27
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.
Case summariesa
Year
Predicted
Value
Latitude Predicted
Value
Length Predicted
Value
Depth
Predicted
Value
Magnitude Predicted
Value
1
2002.13197
.
.
.
.
2
2002.39475
.
.
.
.
3
2002.63362
.
.
.
.
4
2002.89641
.
.
.
.
5
2003.13528
.
.
.
.
6
2003.9807
.
.
.
.
7
2003.63695
.
.
.
.

Ricardo Osés Rodríguez et al., Sci Res Jr Med Sci; Vol-2, Iss-2 (Mar-Apr, 2022): 32-40
38
8
2003.89974
.
.
.
.
9
2004.13863
.
.
.
.
10
2004.40144
.
.
.
.
11
2004.64036
.
.
.
.
12
2004.90322
.
.
.
.
13
2005.14221
36.80002
140.94320
.
.
14
2005.40519
37.51540
141.46654
.
6.64277
15
2005.64437
36.66750
142.06689
.
6.75522
16
2005.90766
37.54633
141.22993
68.23639
6.86805
17
2006.14734
33.72084
141.06731
23,85464
6.71396
18
2006.41145
32.38688
139.90481
11.58168
6.68649
19
2006.65245
32.69383
139.22113
75.17745
6.68672
20
2006.91869
36.48288
138.36089
48.26886
6.71537
21
2007,16315
35,51297
138,55764
71.28674
6.81380
22
2007.43498
34.53478
137.89418
21.07020
6.64605
23
2007.68849
38.02940
139.19448
118.18463
6.70239
24
2007.97494
40.20898
138.27890
35.82580
6.68895
25
2008.25213
32.74544
135.74286
135.36327
6.73127
26
2008,57689
35,53977
136,56612
5.98980
6.63366
27
2008.91606
36.34732
137.11849
82.20294
6.61985
28
2009.34112
33.75918
135.95760
83.32762
6.71865
29
2009.84257
35.84768
136.86200
55.53033
6.67679
30
2010.53020
36.91080
135.41802
22.49965
9.00000
31
2011.45650
32.30861
133.63152
78,14867
6.69164
32
2012,83156
37,13569
133,66066
57,08119
6,59403
33
2014.87013
36.74008
134.16665
222.39738
6.72052
34
2018.04489
37.80706
133.77518
-201,63951
6.63694
35
2022.99545
34.47165
133.79251
144.68870
6.73537
36
2030.88189
36.60188
132.99172
71.14946
6.67985
37
2043.45610
36.09635
133.55142
94.59814
6.73619
38
2063.67788
26.99911
131.60662
133.86037
6.66664
39
2096.21109
29.87414
131.82307
-1.47959
6.77910
Total
N
39
27
27
24
26
a. Limited to the first 100 cases.
4. CONCLUSIONS
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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