Open Access is an initiative that aims to make scientific research freely available to all. To date our community has made over 100 million downloads. It’s based on principles of collaboration, unobstructed discovery, and, most importantly, scientific progression. As PhD students, we found it difficult to access the research we needed, so we decided to create a new Open Access publisher that levels the playing field for scientists across the world. How? By making research easy to access, and puts the academic needs of the researchers before the business interests of publishers.
We are a community of more than 103,000 authors and editors from 3,291 institutions spanning 160 countries, including Nobel Prize winners and some of the world’s most-cited researchers. Publishing on IntechOpen allows authors to earn citations and find new collaborators, meaning more people see your work not only from your own field of study, but from other related fields too.
To purchase hard copies of this book, please contact the representative in India:
CBS Publishers & Distributors Pvt. Ltd.
www.cbspd.com
|
customercare@cbspd.com
This chapter considered monitoring human health condition as vital variable for well-being of man/society required input data for effective daily planning. Researchers have contributed to prediction of incidence/recovery rate for malaria mortality. Modified state-estimation model based (matrix-formulation, weighted sum of squares of errors) was applied. The instrument (sphygmomanometer, etc.) is manipulated for study under investigation to examined existing state of system. Four (4) measurements data were analyzed from different geographical locations for patients with malaria endemic cases. Physician measurement data are implemented into modified state-estimation equations to estimate degree of error(s) to classify as bad measurement. Results shows bad data estimation attributed to poor instrument calibration, aging, and poor physician measurement. These reveal discrepancies between actual (true-measurement) and patient-physical measurements. Four vital measurements include blood pressure (Bp), blood sugar level (BSL), body temperature (BT), and Plasmodium ViVax with relied validation test following chi-square distribution for 2-degree freedom with 99% significance level suspected as error measurement. Model-matrix coded in MATLAB gives state-estimation results x1=8.5225andx2=13.235, indicating strong variation between actual and physical measurements for some patients having low pulse rate under the measurement of blood pressure (Bp). Essentially, physicians’ measurements must be revalidated for accuracy before drugs prescription/administration to avoid under- or over-dose since patients’ body chemistry varies significantly for different persons.
Department of Electrical Engineering, Rivers State University, Port Harcourt, Rivers State, Nigeria
*Address all correspondence to: braidesepiribo@yahoo.com;, sepiribo.braide@ust.edu.ng
1. Introduction
1.1 Improved state estimation model techniques and governing equations
The analysis and investigation of basic human body diagnosis uses the vital statistics variables of physical measurement because it deals with scientific application to the life history of communities and nation. That is historical development which is a function of human society can be numerically be expressed qualitatively or quantitatively. The purpose of this study is to find out the changing composition of communities or nations with reference to sex, age, education, economic and civic status which is considered under study [1].
Evidently the state estimation model considered the numerical records of marriage, births, sickness and deaths by which the health and growth of community may be studied. The vital statistics variable provides the results of the biometry which deals with data and the laws of human mortality, morbidity and demography [2].
This technical contents considered the data or the laws which explain the phenomenon of birth, deaths, health and longevity, composition and concentration etc.
This study can also be extended to solve information particularly on fertility, mortality, maternity, urban density which is indispensable for planning and evaluation of the schemes of health, family planning and other vital amenities for purpose of efficient planning, evaluation and analysis of various economic and social policies [3].
Importantly, data collected on life expectancy at various age levels is helpful in actual calculations of risk on life policies, this means that life table called the biometer of public health and longivity helps in fixing the life insurance premium rates at various age level.
The modified state estimation model described the estimation strategy using different mathematical matrics operations to estimates the physical measurements carried out by a physician/medical doctors, on the view to determine the estimated physical measurements for malaria mortality in a developing countries, the question is how true? is the physical measurement taken by the medical doctor for purpose of placing drug dispensation and administration evidently, research studies has provided with results the measurement equations characterizing the meter readings with the view to the addition of error terms to the system model for purpose of validating physical measurement by medical practitioners [4].
Several measurement instruments and devices are used in the measurements of vital statistics variable (state-variables) of the human life expectancy. We have the sphygmomanotreter (device that measures blood pressure) thermometer (device that measures temperature), (blood sugar level), (plasmodium viviax: parasite for malaria) etc. [5].
The physical measurements data are collected from patients in the health/clinic and hospital which are not always true to some extend, the acquired data from the measurements device/instruments contains inaccuracies which is unavoidable since physical measurements cannot be entirely free from random errors or noise. These errors can be quantified in a statistical sense and the estimated values of the quantities being measured are then either accepted as reasonable or not, if certain measurement of accuracy are exceeded because of noise the true values of physical quantities are never known and we have to consider how to calculate the best possible estimates of the unknown quantities [6].
Incidentally, the techniques of least square is often used to best fit measurement data relating to two or more quantities. However, modified equations are developed and formulated to characterize measurements of the physical data collected or acquired from patients for purpose of analysis with the integration of errors terms in the system model. The best estimates are choosen which minimizes the weighted sum of squares of the measurement errors [7].
State estimation techniques is the process of determining a set of values for a set of unknown systems (Engineering systems, human being systems, medical systems, biological systems, machine/instruments system etc). State variables are based on certain criterion making use of physical measurements made which are not precise due to inherent error associated with controllers/transducers and sometimes creates redundancy of measurement that does not require assessment of the true-value of the systems state variables [8]. Statistical methods are also used to estimate the true value of the system state variables with the minimum number of variables required to analyze the system in all aspects. The measurements taken by a medical practitioner are required to meet the basic records for a given circumstances intended to address particularly to the engineering systems, medical system, biological systems and related systems in order to provide good quality of reliable physical measurements for system variables [9]. Evidently, the necessary conditions for vital statistics variables analysis for administering drugs dispension to patients ensure and declared measurements records conformity to calculation of the measuring instruments, precision and tolerance for purpose of standard practice for world health organization (WHO) [10].
Importantly, if the measurement instruments introduces errors while undertaking details information variables statistics about patients status, this may results into wrong presentation of recorded data required for prescription/dispensing of drugs this will eventually results into gradual breakdown of human body system, immunity, antibodies vital tissues and sensitive organs like liver, kidney etc. in a colossal decay condition that may leads to early mortality for associated emergence of infected and transmitted diseases [11].
Essentially for purpose of good working condition of human lives, standard practice for healthy living, is strongly monitored in order to regularly checked for recalibration of measuring instruments, for purpose of high precision, tolerance and accuracy [12].
3.1 Model formulation of modified state estimation equations
The measurement set used by medical practioners consists of thermometer reading z1, sphygmomanometer z2, Blood-sugar level z3 and plasmodiums vivax parasite transmission measurement z4 etc. Where z1,z2,z3andz4, are mathematical measurement parameter sowing to the physical measurements/quantities respectively.
Similarly, the symbol x represents physical quantities being estimated.
Then the measurement equations that is characterizing the meter readings/measured terms are found by adding error terms (e) to the system model as:
Z=Hx+eE1
Z: Measurement variables.
H: rectangular matrice operations.
x: State variables (the physical quantities being estimated).
e: errors term.
hx: True values of system model.
The numerical coefficient are determined by the human body circulatory components and the error terms e1,e2,e3ande4 which represents errors in measurement z1,z2,z3andz4 and respectively.
If the errors terms e1,e2,e3,e4 are zero, then it is an ideal condition which mean that the meter reading of the physical measurement taken by the vital statistics variable of the patients are exact and true measurements z, which gives exact values of χ1andχ2ofχ̂1andχ̂2 which could be determined.
From the relationship of eq. (1) it can be obtained as:
Z1=h11x1+h12x2+e1=Z1,true+e1E2
Z2=h21x1+h22x2+e2=Z2,true+e2E3
Z3=h31x1+h32x2+e3=Z3,true+e3E4
Z4=h41x1+h42x2+e4=Z4,true+e4E5
Where; Zjtrue: True value of the measured quantity Zj.
Reformulating eq. (2)–(5) into vector form to obtained as;
Which represents the error term between the actual measurement z. and the true (but unknown) values ztrue≜Hx of the measurement quantities. The true values of x1andx2 cannot be determined but we can calculate the estimates χ̂1andχ̂2
Substituting these estimates χ̂1andχ̂2 into eq. (6) gives the estimated values of the errors in the form as:
The quantitie are estimates of the corresponding quantities.
The vector, ê which represents the differences between the actual measurement z and their estimated values ẑtrue≜Hx, thus in compact form is given as:
ê=z−ẑ=z−Hx̂=e−Hx̂−xE9
The criterion for calculating the estimates χ̂1andχ̂2 can be determined as:
ê=ê1ê2ê3ê4TE10
and
ẑ=ẑ1ẑ2ẑ3ẑ4TE11
Eq. (10) and (11) have to be computed for purpose of estimation analysis.
The techniques can be used to describe algebraic sum of errors to minimize positive and negative operations which may not be acceptable.
However, it is preferable to minimize the direct sum of squares of errors.
To ensure that measurement from meters or data collected of known greater accuracy are considered more favorably than less accurate measurements instrument/device, that is in each term the sum of squares is multipled by an appropriate weighting factor (w) to give the objective function as:
f=∑j−14wjej2=w1e12+w2e22+w3e32+w4e42E12
We select the best estimates of the state variables as those values χ̂1andχ̂2 which cause the objectives functions f to take on its minimum value.
In accordance to the application of necessary conditions for minimizing function f, the estimates χ̂1andχ̂2 are those values of χ1andχ2 which satisfy the equations as;
That is, the notation: x̂=0 which, indicates that the equations have to be evaluated from the state estimates x̂=x̂1x̂2T since the true values for the states variable are not known.
The unknown actual error ej are then replaced by estimated errors êj which can be calculated once the true estimate x̂i are known.
Eq. (14) and (15) can be represented in vector form as:
Using the operation of the compact notation process of eq. (9) can be applied to also represent eq. (17) as:
HTWê=HTWz−Hx̂=0E17
Multiplying through this eq. (17) and solving for the estimates (x̂) as:
x̂=x̂1x̂2=HTWH⏟G−1=HTWZ=G−1HTWZE18
Where x̂1andx̂2 are the weighted least square estimates of the state variables, It is the rectangular matrix component
The symmetrical matrix (called the gain-matrix, G) must be inverted as a single entity to give as:
G−1=HTWH−1E19
Which is also symmetrical in the mathematical operations.
Essentially, the weighted least-squares procedure are required to estimates x̂i how close to the true value xi of the state variables,
The expression for the difference xi−x̂i is found my substituting for;
Z=Hx+eto obtain asE20
x̂=G−1HTWHx+e=G−1HTWHx⏟G=G−1HTWeE21
It is an important consideration to check the useful operation of the dimensions of each term in the matrix product of eq. (21) which is an important idea for developing properties of the weighted least-square estimations. In this analysis we have the matrix operation: G−1HTW which as an overall operation of row × column dimensions of 2 × 4, which means that any one or more of the four errors e1e2e3e4 an influence the difference between each state estimates.
The weighted least squares calculations spread the effects of the errors in any one measurements to some or all other estimates the characteristics is the basis for detecting bad data measurement.
In a similar manner we can compare the calculated values of ẑ=Hx̂ of the measured quantities with their actual measurements (z) by substituting for x̂=x from eq. (21) into eq. (7) to obtain as:
In reality we know absolutely true state of a physical operating system. Great care is taken to ensure accuracy. Unavoidable random noise enters into the measurements process to distort more or less the physical results. Repeated measurements of the same quantity under careful controlled conditions reveals certain statistical properties from which the true value can be estimated [13].
If the measured values are plotted as a function of their relative frequency of occurrence, a histogram is obtained to which a continues curve can be fitted as the number of measurement increases theoretically to any number [14].
The continuous curve commonly encountered is a ball-shaped function p(z). This is the Gaussian or normal probability density function gives as:
pz=152πε−12z−μδ2E23
The probability that z-takes on values between the point a and b in Figure 1 is the shaded area given as;
Figure 1.
Gaussian normal distribution.
pr=a<z<b=∫abpzdz=1σ2π∫abε−12=1σ2πE24
The total area under the curve p(z) between 0 and equals to 1. The value of z is certain with probability equal to 1 or 100% [15].
The Gaussian distribution plays a very important role in the measurement statistic because the probability function density cannot be directly integrated. For transfer from z to y using change of variable formula given as (Tables 1–3) (Figure 2):
K
0.05
0.025
0.01
0.005
1
3.84
5.02
6.64
7.88
2
3.99
7.38
9.21
10.60
3
7.82
9.35
11.35
12.84
4
9.49
11.14
13.28
14.86
5
11.07
12.83
15.09
16.75
6
12.59
14.45
16.81
18.55
7
14.07
16.01
18.48
20.28
8
15.51
17.54
20.09
21.96
9
16.92
19.02
21.67
23.59
10
18.31
20.48
23.21
25.19
11
19.68
21.92
24.73
26.76
12
21.03
23.34
26.22
28.30
13
22.36
24.74
27.69
29.82
14
23.69
26.12
29.14
31.32
15
25.00
27.49
30.58
32.80
16
26.30
28.85
32.00
34.27
17
27.59
30.19
33.41
33.72
18
28.87
31.53
34.81
37.16
19
30.14
32.86
36.19
38.58
20
31.41
34.17
37.57
40.00
Table 1.
Normal chi-square distribution table (values of area α to the right of χk2=χk,α2.
A
Pr(a)
a
Pr(a)
.05
0.01994
.08
0.28814
.10
0.03983
.85
0.30234
.15
0.05962
.90
0.31594
.20
0.07926
.95
0.32894
.25
0.09871
1.00
0.34134
.30
0.11791
1.05
0.35314
.35
0.13683
1.10
0.36433
.40
0.15542
1.15
0.37493
.45
0.17364
1.20
0.38493
.50
0.19146
1.25
0.39435
.55
0.20884
1.30
0.40320
.60
0.23575
1.35
0.41149
.65
0.24215
1.40
0.41924
.70
0.25804
1.45
0.42647
.75
0.27337
1.50
0.43319
1.55
0.43943
2.30
0..48928
1.60
0.44520
2.35
0.49061
1.65
0.45053
2.40
0.49180
1.70
0.45543
2.45
0.49286
1.75
0.45994
2.55
0.49379
1.80
0.46407
2.60
0.49461
1.85
0.46784
2.65
0.49534
1.90
0.47128
2.70
0.49597
1.95
0.47441
2.75
0.49653
2.00
0.47726
2.80
0.49702
2.05
0.47982
2.85
0.49744
2.10
0.48214
2.90
0.49781
2.15
0.48422
2.95
0.49813
2.20
0.48610
3.00
0.49841
2.25
0.48778
0.49865
Table 2.
Gaussian distribution for chi-square distribution.
Location/geographical region
Clinical suspected census
Laboratory confirmed cases
Positive predictive accuracy
Buguma city/south
161
28
17%
Ido town/south
223
64
30%
Abalama/south East
181
26
15%
Elelelema town/south east
32
6
20%
okpo town/south
13
3
24%
Sama/south east
45
13
30%
Kala-Ekwe town/south
4
2
5%
Efoko/south
33
1
3%
Tombia town/south east
8
0
0%
Table 3.
Data collected from geographical location about laboratory confirmed cases.
The data collected from different geographical location for patients by a physician on malaria epidemic cases were estimated using the developed modified state estimation model for malaria mortality. The measurement statistics are z:z1=1.5=12080mmHg,z2=1.5=12080mmHg,z3=1.8=14080mmHg,z4=1.9=15080mmHg while the estimated measurement the model ẑ:ẑ1=1.4759,ẑ2=1.4759, and ẑ4=1.87295. The state estimates of the body blood pressure were determined as x1,x2:8.5225and13.235 for the respective patients under study, which indicate low-pulse rate or heart rate that required attention, which is also agree with the validated results of the coded matrix laboratory (matlab results) (Figure 3).
Figure 3.
A bar chart showing clinical/laboratory confirmed cases.
5.1 Expected values of measurements
We assume that the noise terms e1,e2,e3,ande4 are independent Gaussian random variables with zero means and the respective variances σ12,σ22,σ32andσ42 of the physical measurement are considered (Figure 4). Two variables are termed independent when Eeiej=0fori≠j. The zero mean assumption implies that the error in each measurement has equal probability of taking on a positive and negative values of a given magnitudes (Figure 5).
Figure 4.
A chart showing positive prediction for clinical/laboratory cases.
Figure 5.
A line chart showing distribution of clinical/laboratory cases.
The analysis of the vector e and its transpose eT=e1e2e3e4 can be represented as (Figure 6):
Figure 6.
Algorithms (flow-chart for modified state estimation model for malaria mortality showing different measurement system plan.
The expected value of eeT are found by calculating expected value of each entry in the matrix operations.
The expected value of all the off diagonal events are zero because errors are assumed to be independent, the expected values of the diagonal events are non zero and correspond to the variance: Eej2 for i from 1 to 4.
The resultant diagonal matrix are usually assigned the (R) given as:
EeeT=R=Ee12....Ee22......Ee32..Ee42E27
=σ12....σ22......σ32..σ42E28
Evidently, the statistical properties of the weighted least-square estimation provides solution to the measurement z, which is the sum of the Gaussian random variables e1 and the constant term h11x1+h12x2 which represents the true values Z1true of Z1. The addition of the constant term to shift the curve of e1 of the right by the amount of the true value.
Weighting Factor w
The analysis of formulating the objective function f, the preferential weighting wi is given to be more accurate measurement by choosing the weight wi as the reciprocal of the corresponding to the variance δj2. This means that an errors of smaller variance have greater weight w, hence we can specify the weighting matrix, w as:
W=R−1=1δ12....1δ22......1δ32..1δ42E29
The, gain matrix becomes
G=HTR−1HE30
The weighted sum of square of error as the objective function f, determination.
The critical value of the statistics f can be determined using the tabulated values of χk,α2 for a quantifiable level of significance, k: degree of freedom Nm−Ns. That is the calculated value can be compared to the tabulated value to measure accuracy which is given as:
prf≤χk,α2=1−αE31
The weighted sum of squares equation of errors with weight wi choosen equals to the reciprocal of corresponding error δj2 variance which is given as:
Where: h1,h2,h3 and h4 are function that expresses the measured quantities in terms of the state variable while e1,e2,e3ande4 are Gaussian random variables terms. The true value of χ1amdχ2 and not known and have to be estimated from measurement: Z1,Z2,Z3andZ respectively.
Chi-square test statistics (f), as a sum of squares of error terms for purpose of validation
The analysis of physical measurement, the chi-square distribution test and validation are required to the check the presence of bad data. Then eliminate any bad data detected and recalculate subsequent resultant state estimation from the determined results.
The objective function (f) for chi-square distribution can be presented as:
f̂=∑j−1Nêj2σj2=w1ê12+w2ê22+w3ê32+w4ê42E33
where;
w=1σ2
σ: variance of measurement error
α: quantifiable level of significance for accuracy
f≤χα,k2: for a quantifiable level of significant α for a given degree of freedom k. If f is greater than χα,k2 then there is at least suspected bad data measurements in the analysis which required attention.
This means that the suspected measurement instrument (z) must be recalculated and subjected to test statistics and required re-measurement of the vital statistics variables of the system.
This could be traceable to human error, instrument error due to poor calibration, aging of the instrument and temperature/humidity etc.
If f≤χα,k2 is satisfied it is adequate for purpose of physical measurement accuracy, while comparing calculated and tabulated values for validation.
Standardized error estimates
The standardized error estimations can be determined using diagonal elements as:
ê1R11′=Sde1
ê2R22′=Sde2E34
ê3R33′=Sde3
ê4R44′=Sde4
Analysis of measurement for malaria mortality Using modified state estimation model
The measurement equations characterizing the physical status of patient using sphygmomanometer for blood pressure considered the true/actual value of the system model and the addition of error term in the system model were developed. The question is how true is the physical measurement carried out by the physician? Which can be represented as:
Z=hijxi+ℓiE35
Z: Measurement of the vital statistics variable of the patients.
hij: Account for the precision of the measurements to the accuracy of the instruments (how close to the true value).
xi: Unknown state variable that need to be determined and accounts for the pulse/health rate for blood pressure measurement.
ℓi Error term introduced in the measurement which can be expressed mathematically as:
Z=h11x1+h12x2+e1E36
Eq. (36), provided the vital statistics variable measurement which is the weighted sum of squared of errors for the Gaussian distribution. Since the physical measurements of the patients is considered as a function of their relative frequency of occurrence, a histogram may be represented which is a continuous curve in relation to the number of occurrence.
Clinical Diagnosis Measurement, geographical location and distribution.
Data were collected from reputable hospitals and clinics from different location for malaria mortality using blood pressure measurements as one of the key associated parameter for the incidence of malaria parasite transmission variable (Tables 4–6).
S/N
Location/Geographic region
Clinical suspected census (%)
Laboratory confirmed
Positive predictive accuracy
1
Buguma city/South
161(23)
281 (0)
17% (10–24)
2
Ido town/South
223(32)
64(45)
30% (24–35)
3
Abalama/South East
181(26)
26(18)
15% (10–20)
4
Elelema town/south-Cast
32(5)
6(4)
20% (8–36)
5
Okpo town/south
13(2)
3(2)
24%(6–54)
6
Same south-east
45(6)
139
30%(16–44)
7
Kala Ekwe town/south
4(0.6)
2(1)
5%(7–93)
8
Efoko/South
33(5)
1(0.7)
3%(0.1–16)
9
Tombia/South
8(1)
0
0%(0–37)
Total
700
143
Table 4.
Distribution of suspected and confirmed cases of malaria parasites (plasmodium) according to the province in a developing countries.
S/N
Vital statistics variables for measuring transmitted cases of malaria parasite (plasmodium) etc
Blood (BP) Pressure Measurement
Accepted standard for blood pressure measurement.
1
Measurement 1; patients - A: Abuja City in Nigeria
12080mmHg=1.5
Ok (normal)
2
Measurement 2; patients –B Buguma City in Nigeria
12080mmHg=1.5
Ok (normal)
3
Measurement 3; Patients –C Lagos City in Nigeria
14080mmHg=1.8
Required attension
4
Measurement 4: Patients – D Port Harcourt City in Nigeria
15080mmHg=1.9
Required attension
Table 5.
Blood pressure measurement (Sphygmomano-meter) for purpose of incidence of malaria parasite transmission.
S/N
Measurements instrument Sphygmomanometer (BP)
Precision to the accuracy of measurements instruments
1
Measurements 1, Blood pressures for pulse rate estimation –Abuja City in Nigeria
8% & 6% to the true values of the system model measured
2
Measurement 2, blood pressure for pulse rate estimation –Buguma City in Nigeria
8% & 6% to the true values of the systems model measured
3
Measurements 3, blood pressure for pulse rate, estimation –Lagos city in Nigeria
9% & 6% to the true values of the systems model measured
4
Measurement 4, blood pressure for pulse rate estimation –Port Harcourt City in Nigeria.
8% & 9% to the true values of the system model measured
Table 6.
Sphygmomanometer measurement and precision for true (actual value of measurement) for associated malaria parasite transmission.
Case 10: Determination of number of physical measurement Nm and states variable Ns on the view to determine redundancy K for a quantifiable level of significance.
Nm=Z1,Z2,Z3andZ4=4(four physical measurements)
Ns=x1&x2=2 (blood pressure for pulse/heart rate)
RedundancyK=Nm−Ns=4−2=2E67
Case 11: Determination of errors estimatesê of the physical measurements and estimated measurementsẑ are presented as:
Case 12: Determination of sum of Squared of Errors e Measurement
If calculated weighted sums of squares of errors calculated fcalculated is greater than chi-square distribution it can be deduced that there is suspected error (or bad data in the measurement sets).
Similarly,
If calculated objective function fcalculated is less than chi-square distribution value, it is concluded or declared a violations which does not satisfy the measurements criteria for decision making for purpose of diagnosing human body conditions.
The chi-square distribution from tabulated results given as: χk,α2=9.21
fcalculated≤χk,α2
where;
K=Nm−Ns=4−2=2
For, α = 1% quantifiable level of significant = 0.01α=0.01
(Significance level, α=0.01)
The probability of 1−α=1−0.01=99% declared confidence level for a degree of freedom, K=Nm−Ns=2
From the tabulated result obtained for a given degree of freedom and a quantifiable level of significance of α=0.01, for k=2 given as 9.21 which means that the calculated value of fcalculated is greater than the critical value of the chi-square distribution value. Thus, the chi-square of f provides a test statistics for validating the error measurements of bad data or probably suspected adverse health condition that required attensions for purpose of ensuring good status healthy conditions.
%MATTIX LABORATORY
%PROGRAM: MATLAB FOR MALARIA MORTALITY
%AUTHUR: BRAIDE, SEPIRIBO LUCKY
%TECHNICAL PAPER PORESENTAION
%First iteration calculation using a flat start values (,k,t which
%represent the static variables x1 and x2);
k = 1;
t = 1;
% measurement instrument represented as z: z1 z2 z3 z4
z1 = 1.5;
z2 = 1.5;
z3 = 1.8;
z4 = 1.9;
z = [1.5; 1.5; 1.8; 1.9];
% estimated measurement represented as zk1 zk2 zk3 zk4
zk1 = 1.4759;
zk2 = 1.4759;
zk3 = 1.825825;
zk4 = 1.87295;
% measurement error represented as e1 e2 e3 e4
e1 = z1-zk1;
e2 = z2-zk2;
e3 = z3-zk3;
e4 = z4-zk4;
% Jacobianmatrix represented as H
H = [0.08 0.06;0.08 0.06;0.09 0.08;0.08 0.09];
%Transpose of jacobian matrix T represented as H
T = H′
% Diagonal matrix of the weighting factor as W
W = [100,0,0,0; 0,100,0,0;0,0,50,0;0,0,0,50];
% MUutiply Transpose of jacobian matrix H′ and weighting factor W as
D=H′*W
% Multiply the matrix operation D and jacobian matrix H to obtain gain matrix represented as
G = D*H
% The inverse of gain matrix G represented as F
F = inv.(G)
% multiply the matrix operation F and matrix D be represented as
M = F*D
% multiply matrix M and Z representation as N = M*Z state variable [xi x2]
% Determination of matrix operation of state estimation [x1 x2] = N
Considering the fact that health is wealth the relationship between the two is frequently misconstrued. That is there is strong need for healthy living to create wealth for man and society.
Measurement of malaria endemictiy is basically on vector or parasites measurement especially for infected cases on transmission of plasmodium parasite etc. which may seriously leads to some vital sign and symptom: Temperature rise beyond normal level, headache, blood pressure become abnormal, blood-sugar concentration level may also be affected medically etc.
Evidently, the mapping of malaria transmission have demonstrated a wider geographical distribution of the parasite (plasmodium, etc). The number of clinical report cases due to malaria infection resulted into early mortality which is becoming an increase on daily basis across the world. Particularly in south America, where P. Vivax is currently the most predominant malaria species. Although control measures and programs have had a significant impact on malaria associated cases. Consequently the centers for disease control and prevention (CDC) Saving lives, protecting people in various states of America have considered regular, rapid and accurate diagnosis of malaria which is an integral part to the appropriate treatment of affected individuals. It is also requested that the CDC: Health care providers should always obtain a travel history form patients, especially person who traveled in a malaria epidemic area, must be evaluated for check using appropriate tests (for malaria) for purpose of healthy free environment. This technical paper having carried out thorough extensive investigation especially to this robust medically affected case of earthly malaria mortality for man which may also be associated to bad measurement for vital statistics variables about a patients. The detail history of patients measured must be checked for accurate, precision, tolerance, error etc. to the true value declared by standard world health organization (like WHO etc). Therefore physical measurements taken by medical practioner from patient must:
Regularly check for instrument calibration measurement for effectiveness before drug prescription/administration.
Consider and satisfy many associated variables measurement to the particular emergence of incidence of malaria species before placing drugs administration and dispensing to avoid over-does or under-dose problems which may leads to early malaria mortality.
Considering adequate treatments procedures for malaria cases which may depends on disease severity, species of malaria parasites infections on the view to determine the organism that is resistant to certain anti-malarial drugs in order to provide adequate alternative provisions.
Check for vaccine effectiveness to affected cases of malaria patients particularly to age, sex, community (habitant or group of people) and other associated multivariable’s parameter like vaccination histories etc. to avoid gradual destruction of sensitive organs like liver and kidney etc.
Check for bad data measurement: the status of human body state which may be affected by surrounding circumstances, aging of measuring instrument, human error, temperature/humidity, sensitivity of measurement etc.
This work can also be extended to include the estimation of malaria mortality the estimation of malaria mortality and recovery rates of plasmodium falciparium parasitaemic, using the model equations:
The transition rates: handr can be estimated from transition frequencies: αandβ with
The analysis of modified state estimation model is developed for estimated measurement of malaria mortality in a case of a developing countries. This model help to identify detect and flag measurement error which is classified as bad data measurement; whose result may be received on drug prescription and administration for early malaria mortality rate especially when measurement instruments are not regularly calibrated for efficiency. This technical paper for purpose of analysis and scope considered the associated vital statistic variables like blood-pressure (BP) using sphygmomanometer as a key driver for this analysis. The techniques establishes a mathematical modified state estimation model that characterizes the physical measurement of the patient to the acceptable value of BP=12080mmHg in order to satisfy the operating normal conditions.
The true value of the system model equations and error term addition are considered for purpose of estimating measurements made by physician instrument. Data were collected from four (4) geographical area in a developing countries for purpose of validation of the modified estimation model. The techniques allow for an algebraic summation operation of measurement for the weighted sum provided the declared standard measurement of blood pressure of 120mm80Hgis not violated.
The analysis technical paper identified bad data measurement which required urgent attention for check: The surrounding circumstance of the patients, human error, calibration error etc. for the purpose of determining the state of the body system configuration.
The paper also validated this work research via the objective function f as the calculated value versus chi-square distribution (tabular form) for 99% level of significance with 2 degree of freedom in quantitative measures.
This paper also establishes a string conformity, uniquencie and synergy between measured ad estimated measurements which eventually validated with objective function calculated f and chi-square distribution and between matrix operations and matrix laboratory code programs for a test statistics.
References
1.World Health Organization. Global Malaria Programme: World Malaria report. 2011. Available from: http://www.who.int/malaria/World malaria/WMR2011noprofiles lowres.pdf
2.Braide SL, Idoniboyeobu DC. Determinants of estimated measurement for malaria mortality using modified state estimation model in a case of a developing country. In: Proceedings of the World Congress on Engineering and Computer Science. San Francisco, USA; WCECS; 22-24 Oct 2019. ISBN: 978-988-14048-79, ISSN: 2078-0966 (Online)
3.Guerra CA, Snow RW, Hay SI. Mapping the global extent of malaria In 2005. Trends Parasltology. 2006;22:353-358
4.Marques AC. Human migration and the spread of malaria in Brazil. Parasitology Today. 1987;3:166-170
5.Alves FP, Durlacher RR, Menezes MJ, Kriger H, Silva LHP, et al. High prevalence of asymptomatic plasmodium wax and plat infections in native amazonian populations. The American Journal of Tropical Medicine and Hygiene. 2002;66:641-648
6.Qliveira-Ferr Bira J, Lacerda MVO, Brasil P, Ladislau JLB, Tauil PL, et al. Malaria in Brazil: an overview. Malaria Journal. 2010;9:115
7.Coura JR, Suarez-Mutis M, Ladeia-Andrade S. A new challenge for malaria control in Brazil: Asymptomatic plasmodium infection. Memorias do Instituto Oswaldo Cruz. 2006;101:229-237
8.Braide SL, Idoniboyeobu DC. Gas turbine blade reliability of generator availability for electric power supply using optimal estimation of Weilbull probability distribution. Internal Journal of Scientific & Engineering Research. 2022;13(3):340-357
9.Price RN, Tjitra E, Gunrra CA, Young S, Whlto NJ, et al. Vivax malaria; neglected and not benign. The American Journal of Trc Hygiene. 2007;77:79-87
10.Guerra CA, Howes RE, Patll AP, Gething PW, Van Boeckel TP, et al. The international limits and population at risk of Plasmadi transmission in 2009. PLoS Neglected Tropical Diseases. 2010;4:e774
11.Braide SL, Idoniboyeobu DC. Development of error estimation model (ESM) for radial distribution system. International Journal of Academic Research. Sept 2011;3(5):439-452
12.Mueller I, Gallnski MR, Baird JK, Carlton JM, Kochar DK, et al. Key gaps in the knowledge of plasmodium vivax, a neglected h parasite. The Lancet Infectious Diseases. 2009;9:555-566
13.Ladeia-Andrade S, Ferreira MU, De Carvalho ME, Curado I, Coura JR. Age-dependent acquisition of protective immunity to man populations of the Amazon Basin of Brazil. The American Journal of Tropical Medicine and Hygiene. 2009;80:452-459
14.Silva-Nunes M, Moreno M, Conn JE, Gamboa D, Abeles S, et al. Amazonian malaria: Asymptomatic human reservoirs, diagno environmentally driven changes in mosquito vector populations, and tho mandate for sustainable control strategies. Acta Tropica. 2012;121(3):281-291
15.Brasil P, Costa AP, Pedro RS, Bressan CS, Silva S, et al. Unexpectedly long incubation period of plasmodium vivax malaria, in chamoprophylaxis, in patients diagnosed outside the transmission area in Brazil. Malaria Journal. 2011;10:122
Written By
Sepiribo Lucky Braide
Submitted: 27 July 2022Reviewed: 11 August 2022Published: 20 September 2022
Open access peer-reviewed chapter
