In this study, a continuous mathematical model for the dynamics of Tuberculosis at a varied recruitment
rate
bN
was formulated. In the model, we partitioned the population into Susceptible (S), Vaccinated
(M), exposed (E), Infected (I) and recovered (R) individuals. We analyzed a SMEIR compartmental
nonlinear deterministic mathematical model of Tuberculosis epidemic in a community with constant
population. Analytical studies were carried out on the model using the method of linearized stability. The
basic reproductive number
R0
that governs the disease transmission is obtained from the largest
eigenvalue of the next-generation matrix. The disease-free equilibrium is computed and proved to be
locally asymptotically stable if
R0 > 1
and unstable if
R0 > 1
. Finally, we simulate the model system in
MATLAB and obtained the graphical behavior of the infected compartment at different levels vaccination
and treatment rates. From the simulation, we observed that the Tuberculosis infection was eradicated
when
R0 > 1
while it persist in the environment when
R0 > 1.
keywords: : Tuberculosis, SMEIR Model, Basic reproduction number, Local stability, numerical
simulation
1Department of Mathematics and Statistics, University of Delta and Delta State Nigeria.
2Department of Mathematics, Delta State University, Delta State Nigeria. 3Department of Mathematics and Statistics, Ogwashi-Uku Delta State Polytechnic. Nigeria
Sometimes regression results are non-optimal, biased estimates, increase in Type 1 error rates, poor
standard errors, untrustworthy confidence intervals, and insignificance F and T Test. This is as a result
of assumption violations emanating from multicollinearity among the independent variables. The
variance inflation factor (VIF) of predictors are appropriately high (X1= 50.603) and (X2= 49.286).
They are above the threshold value of 10+. The bivariate scatter plots shows evidence of 45 degree
linear relationship between Trademark(X1) and Bread Texture(X2). The Bivariate Correlation suggests
that a strong correlation exist between X1 and X2 of 0.990 (r= 0.990) exceeding the set requirement
of 0.8+. The above diagnostics are signs of multicollinearity present in the linear model. Furthermore,
the significance value for each of the independent variable is greater 0.05 level of significance
showing evidence of multicollinearity and non-normality in the model. The multicollinearity
detention gave birth to other violations hidden in the model. A new diagnostics measures called
adjusted coefficient of determination(𝐴𝑑𝑗𝑟2
) instead of ordinary coefficient of determination(𝑟2
)
were use in the computation of variance inflation factor. However, in all trial transformations,
increase in sample size
(n <= 69)
with linear and quadratic features seems very satisfactorily because
its variance inflation factor (VIF) of each independent variable was less than 2.500 specified-justified
thresholds. These are also accompanied with satisfaction of four classical regressions, optimal
statistical power, feasible partial regression, and residuals plots as well as regression statistics been
improved upon.Therefore, the variance inflation factor of 2.500 below should be used a as a stopping
rule to optimal models, predictive power ability, strong statistical power and all assumptions
satisfaction.
keywords: Model violation, Multicollinearity, Preliminary study, Transformations, Classical
Assumption, Other assumption violations.
ChatGPT is a conversational language model that can interact with users naturally and engagingly. It is
based on GPT, a large-scale neural network that can generate coherent and diverse text from a given prompt.
ChatGPT is trained using reinforcement learning from human feedback, which allows it to adapt to different
contexts and preferences. However, ChatGPT also faces some limitations and challenges, such as producing
inaccurate or nonsensical answers, being sensitive to input phrasing, and being over-verbose or repetitive.
In this paper, we propose to view ChatGPT as a fuzzy system, which can capture the uncertainty and
ambiguity inherent in natural language. We argue that fuzzy logic and fuzzy sets can provide a useful
framework for analyzing, evaluating, and improving ChatGPT’s performance and behavior. We illustrate
how fuzzy concepts such as membership functions, linguistic variables, and fuzzy rules can be applied to
ChatGPT’s input, output, and internal representations. We also discuss some potential benefits and
drawbacks of using fuzzy methods for ChatGPT, as well as some open questions and future directions for
research. keywords: fuzzy, ChatGPT, inference, fuzzify
The conventional Caesar cipher, traditionally reliant on alphabet letters, has undergone a modification in
this undertaking. The innovation involves the incorporation of both alphabets and special characters,
resulting in a robust cipher text. This alteration serves a dual purpose: facilitating uncomplicated
decryption for the intended recipient while presenting a formidable challenge for potential intruders, by
expanding the character set to encompass special characters, the cipher attains heightened complexity.
This not only enhances the security of the encoded message but also fortifies the resilience against
unauthorized deciphering attempts. The strategic utilization of special characters introduces an additional
layer of intricacy, rendering the cipher less susceptible to conventional decryption methods. The primary
objective remains to create a cryptographic system that strikes a delicate balance between accessibility
and security. The intentional inclusion of special characters not only diversifies the encoding possibilities
but also contributes to the creation of a dynamic cipher system. This adaptive approach ensures that the
communication remains safeguarded against adversaries seeking to compromise the confidentiality of the
information. In essence, this evolved Caesar cipher becomes a potent tool in the hands of the sender and a
formidable enigma for those attempting unauthorized access.
Six regression models have been utilized in this particular research to check for the existence of
correlation in model residual using secondary data on Nigeria Gross Domestic Product at Current Basic
Prices. The appropriate model for this investigation is the Sine design that has the very least mean square
error, the very least standard deviation, smallest AIC, smallest BIC and HQC, although the particular
design contains the greatest R2
valued while the Cosine design has the greatest Durbin Watson statistical
value, but many parameters came up because of transformation effect. It was concluded from this study
that the sine transformation technique could be more effective in solving the issue of autocorrelation in
real life data. Therefore, it was suggested that much more comprehensive work be performed making use
of other transformation methods not mentioned or even used in this particular current study to determine a
far more appropriate design to be used in the research or for dealing with autocorrelation issues in the
data.
keywords: : Autocorrelation, Residual, Regression Analysis, Statistical Model, Gross Domestic
Product.
The study entitled "Analysis of length of stay of patients in the emergency care unit, Federal Medical
Centre, Umuahia (a case study of Crowther ward)" was conducted to access the probability distribution
that best fits the length of stay of patients in the ward. The data used in this work was secondary data collected
from the Crowther ward of the Federal Medical Centre, Umuahia. The data comprises 100 patients with their
age, date of admission, diagnosis, date of discharge, disposal and number of days in the ward. The number of
days (length of stay) a patient stayed in the ward followed best the Exponential 2 parameter distribution.
We estimated the expected length of stay of patients who entered the ward to be 18 days on average. We found
the age and type of disease to be some factors that influenced the length of stay of patients in the Crowther
ward. Aged patients (patients of the dependent population) and patients diagnosed with fractures
stayed much longer than other patients in the ward. The study therefore recommends that the management
of the Crowther ward, Federal Medical Centre, Umuahia, should provide more bed space and quality and timely
services to patients. Government, churches and other social organizations should educate and sensitize their
members on the implications of road accidents, which will help reduce the rate at which we admit patients into
the Crowther ward and also the length of stay of patients in the ward.
keywords: Length of stay, Prediction, Probability Distribution, Easyfit, Fracture.
In this paper, a model for the transmission dynamics of computer virus is formulated and two control
strategies: a strong antivirus and treatment are deployed to minimize the total number of infected
computers and the cost associated with the control strategies. Optimal control theory is applied to a
system of ordinary differential equations of a computer virus epidemic. The Pontryagin’s maximum
principle is employed to find the necessary and sufficient conditions for the existence of the optimal
controls. Runge-Kutta forward-backward sweep numerical approximation method is used to solve the
optimal control system. The results show that for the computer virus spread to be under control in the area
where it is epidemic,
50%
of the strong antivirus and
50%
of treatment should be continuously
implemented.
keywords: SPEIQRS Model, transmission, Computer, Virus, Pontryagin’s maximum principle, optimal
control, antivirus, treatment, Hamiltonian, numerical simulation.
We presented the notion of graphical revised fuzzy metric spaces in this paper, which is a relation based expansion of revised fuzzy metric spaces. We also explored topological structure and
convergence requirements, as well as proving a Banach fixed-point result in graphical revised fuzzy
metric space. In the framework of graphical revised fuzzy metric spaces, we establish a solution to an
integral equation and nonlinear fractional differential equations using the presented results. We've
included several examples to assist you visualize the results.
keywords: revised fuzzy metric space, fixed point, graphical revised fuzzy metric spaces
This research was carried out to investigate the Statistical Analysis of Diabetic Patients with Foot Ulcer (A
Study of Federal Medical Centre, Umuahia, Abia State). The Federal Medical Center in Umuahia provided
the secondary data for this study, which included censored and deceased diabetic patients with foot ulcers.
The information on foot ulcer kinds, types of ulcers, and sites spans three years, from 2021 to 2023. The
non-parametric survival model was the analytical tool employed in this study. 37.5% of the results were
female, and 62.5% were male. Of these patients, 57.33% were censored and 42.67% of the female patients
passed away. Of the male patients, 54.4% were censored and 45.6% were dead. About 21% of the diabetic
patients in the study had type 1 diabetes, whereas 79% had type 2 diabetes. Of the patients with diabetes,
40.5% had type 1 diabetes and 45.6% had type 2 diabetes at the end of the study. Neuroishemic, ishemic,
and neuropathic ulcers affect 77.5%, 15.5%, and 7.0% of the patients, respectively. 75.5% of the patients
have the ulcer on their forefoot, 12.5% and 12 % have the ulcer on their mid foot and hind foot respectively.
Additionally, statistical studies utilizing the Breslow and log-rank tests reveal no significant differences
across the groups of diabetic complications. The survival plot suggests that patients with neuropathy have
a higher chances of survival to those with other ulcer types, patients with ulcer on their fore foot have a
higher chances of survival to those affected in other area, female patients have a lower chances of survival
to a male patient & diabetic type 2 patients have a lower chances of survival to diabetic type I patient. The
study also found that two significant explanatory factors are ulcer size and age. Based on the findings of
this study, it was recommended that effective health care system should be provided by government at all
levels to meet the needs of diabetic patients and prevent diabetic foot ulcer.
keywords: foot ulcer, diabetes, survival probability, diabetes patients
