In this study, a continuous mathematical model for the dynamics of Chickenpox (Varicella) outbreak at
constant recruitment rate
was formulated. In the model, we partitioned the population into Susceptible
(S), Vaccinated (V), exposed (E), Infected (I), Quarantined (Q) and recovered (R) individuals. We
analyzed a SVEIQR compartmental nonlinear deterministic mathematical model of Chickenpox 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 points of
the model is computed and proved to be locally and globally asymptotically stable if
R0 < 1
and unstable if
R0 > 1
. A sensitivity analysis of the epidemiological model of Chickenpox epidemic is performed in
order to determine which model parameters are the most important to disease transmission. Finally, we
simulate the model system in MATLAB and obtained the graphical behavior of the variables in the
model.
keywords: : Chickenpox, SVEIQR Model, Differential equation Basic reproduction number, Local
stability, numerical simulation
This study presents a method of estimation of adult mortality from non-stable population using the
modified approach to the Preston (1983) integrated method when net migration is not zero. In deriving
the model for estimation of adult mortality from non-stable population, Preston (1983) has assumed that
the study population is closed to migration, that is, the net migration is zero. However, in most
developing countries this assumption is not strictly true. So in this study, we propose a method of
obtaining estimate of adult mortality from a non-stable population when net migration is not zero.
Preston's approach is to relate the characteristics of the observed population to some life table functions
and to obtain estimate of adult mortality from the life table functions. This approach was adopted in this
study to obtain an adjustment factor (
AF
) when net migration is not zero. The adjustment factor is the
ratio of the observed proportion of mid-period population reported as aged x years
(c(x,t))
when net
migration is not zero to the corresponding proportion when net migration is zero(c^(x,t)) This factor
was used to obtain the adjusted life table proportion surviving to age x from age 5 years ((5)P^(x)). Data on
age- sex distribution of populations of three selected developing countries were used to illustrate the
methods. The result show that
5P^(x)
is, at almost all ages, lower for the modified method than the
original Preston's method. It has therefore, been recommended that when net migration is not zero an
adjustment is necessary to obtain a more reliable estimate of adult mortality (the life table probability of
survival to age x from age 5 years 5P^(x)).
keywords: Non-stable population, Life Table Functions, Modified Preston method, Adult Mortality,
Adjustment Factor.
With the advent of machine learning techniques, speech recognition systems have improved drastically.
This study investigates the potential of a hybrid model combining the traditional Hidden Markov Models
(HMMs) and Deep Neural Networks (DNNs) for a more efficient speech recognition. The hybrid model
leverages on the temporal modeling capabilities of HMMs and also on the ability of DNNs to capture
complex acoustic patterns, resulting in improved accuracy, precision, recall, and F1 score in speech
recognition tasks. In other words, the DNNs are trained to estimate the likelihood of observed acoustic
features given the speech signal. The output probabilities of the DNN are then utilized as emission
probabilities in the state modeling of the HMM. Details experimental analysis revealed that, the proposed
hybrid model emerged as the most promising model, consistently demonstrating high accuracy on both
training and validation sets as compared to the traditional HMM and DNNs. An F1 score, reflecting a
balance between precision and recall, remained at a moderate level, indicating a robust trade-off in our
proposed model. Whilst HMM exhibited exceptional training accuracy, there were concerns about potential
overfitting, as the model's performance on the validation set showed some variability. DNN demonstrated
moderate to high accuracy on both sets, suggesting effective learning and generalization. Also, the learning
curve analysis reavealed that, our proposed hybrid model offers a robust approach to capturing language
processes. The findings will pave the way for further developments in speech recognition technology and
provide practical directions for researchers and practitioners in this area of research. keywords: Hidden Markov Model, Speech Recognition, Perfoemance metrics, Hybrid, Neural Network
Six chosen procedures were compared with ANOVA, which was typically used as a backup to ANOVA
(Analysis of Variance) in cases where the assumption of equal variance was not met. The tests Alexander-Govern, Brown-Forsythe, James second order, Welch's heteroscedastic F, Kruskal wallis, Welch's
heteroscedastic F with trimmed means, and Winsorized variances tests are the six procedures that were
chosen. The six procedures and ANOVA were compared using simulated data, type I error rate, and test
power to determine which of the two was the most robust. The criteria were: normally distributed sample;
balance and imbalance; small and large sample; and different significant levels (0.01, 0.025, and 0.05). The
simulation's outcome demonstrates that Welch's heteroscedastic F test with trimmed means and Winsorized
variances test is preferred over others. The simulation result shows that Welch's heteroscedastic F test,
Alexander-Govern test, and Welch's heteroscedastic F test with trimmed means and Winsorized variances
test are almost the same
keywords: Heteroscedastic, Type l Error Rate, Power of the test, Robust, Normal Distribution
The study assessed pre-service teachers’ readiness to adopt artificial intelligence-based pedagogy in
teaching mathematics in Bayelsa State. The study adopted a descriptive survey design. Three research
questions were raised to guide the study. The population of the study was all pre-service teachers in the
three tertiary institutions where mathematics education is studied in Bayelsa State. A sample of 490
respondents drawn from the department of mathematics education in the 3 tertiary institutions was used
for the study. The instrument for data collection was a structured questionnaire styled as “Readiness to
Adopt AI-based Pedagogy Questionnaire (RAAIPQ)"developed by the researcher and validated by
experts. The reliability analysis was done using Cronbach Alpha Formula, which yielded a value of
0.79. The research questions were answered using mean and standard deviation. The findings revealed
that the pre-service teachers’ level of awareness of the use of Artificial Intelligence-based pedagogy for
teaching mathematics in Bayelsa State is low. It was recommended that there is a need for the
management of tertiary institutions to organize and integrate the features of artificial intelligence-based
pedagogy into the mathematics education curriculum
keywords: : Assessment, Availability, Pre-Service Teachers’ Readiness, AI-based Pedagogy
The study investigated the impact of Problem-Based Learning Model on Students' Academic Achievement
in Physics. The study was guided by two research questions that were correspondingly hypothesized. The
study adopted the quasi-experimental design of pre-test post-test non-equivalent control group. The
population of the study was made up of three hundred and one (301) senior secondary school year two
students in Patani Local Government Area, Delta State. A multi-stage sampling technique was used to select
the sample for the study. The first stage involves the use of purposive sampling technique in which schools
were selected to meet certain criteria and four schools were qualified, in the second stage, four intact classes
in each of the schools selected were assigned to control and experimental groups through flipping of the
coin. At the final stage the students in their intact classes form the sample size used for the study. The
sample consisted of 117 students (59 males and 58 females). The instrument used for data collection in the
study was a 25-item multiple choice Physics Achievement Test (PAT) which was designed by the
researcher. The reliability was determined using the Kuder-Richardson formula -20 with a co-efficient
value of 0.819. T-test of independent sample was used to test the hypotheses at 0.05 level of significance.
Results showed that; Students taught Physics concepts with Problem-Based Learning Model performed
better than their counterparts who were taught Physics concepts with lecture method. There was no
significant difference in the mean achievement scores of male and female students taught Physics concepts
using PBL model. It was recommended that Physics teachers should make use of PBL model to facilitate
the teaching of Physics at Secondary School level.
keywords: : Impact, Problem-Based, Learning Model, Academic Achievement, Physics
CHATGPT is a chatbot system that applies the large scale of this pre-trained language model to produce
natural and application-like responses to the users’ messages. The new proposed application called
CHATGPT seeks to offer the user an improved way of practicing generative models and at the same time
engage the user in a fun and resourceful interaction with an artificially intelligent agent. With this tool that
researchers are still exploring, it is our intention in this paper to solve some rather difficult models. We are
much interested to know how these models will advance this smart tool to enable it play a crucial role in
the future. In this paper various versions of the interactive soft set models are explained along with the
scope of effectiveness. It has been determined that the ChatGPT has achieved greater results in terms of
performance in comparison with other instruments that is based on the full concept of AI
keywords: Chatgpt, Soft Set, Dual Hesitant Fuzzy Soft Set, Rough Fuzzy Bipolar Soft Set.
This work presents a new Caesar algorithm that contains alphabet and special characters presents in
QWERTY keyboard combination, within the modified Caesar table. Unlike traditional implementations
of Ceaser table that contains alphabets only, the algorithm employs Modulo 40 instead of Modulo 26 of
the classical Ceaser algorithm, resulting in a ciphertext that includes both alphabetic and special
characters. This modification aims to increase the security of encrypted data by diverting the attention of
cyber attackers using frequency analysis of English letters. The introduced special characters from the
QWERTY keyboard provide an additional layer of complexity, making the encryption more complex to
decryption techniques. The proposed method offers a new perspective on cryptographic algorithms,
contributing to the ongoing efforts to boost cyber security measures against continues attacks
keywords: Ceaser cipher, Encryption, Algorithm, Security analysis, Cyber security.
We consider the problem of finding a pair of functions ℎ(𝑡) and 𝑤(𝑥,𝑡) that satisfy the equation wtt(x,t)-h(t)wxx(x,t)=0 under Cauchy boundary conditions. We will see that an approximate
solution can be found using the techniques of generalized inverse problem of moments and find dimensions
for the error of the estimated solution.
keywords: generalized moment problem; integral equations; hiperbolic equation, Cauchy
conditions.
In This work, a modification of the traditional Vigenère cipher is considered to improve its security
against modern cyber attacks. The classical Vigenère cipher, while historically significant, is open to
frequency analysis and other forms of cryptographic attacks due to its reliance on a repetitive key and
alphabetic ciphertext. To address this weakness, our proposed modification that uses an improved
Vigenere square table which introduces alphanumeric ciphertext, expanding the character set from 26
alphabetic characters to 31 characters, including letters and digits. This increases the complexity and
enhances the security of the cipher, and it can resist frequency analysis and brute force attacks.
Additionally, this modification employs a dynamic key mechanism, which changes with each character
encrypted. Through rigorous testing and analysis, we demonstrate that the modified Vigenère cipher
withstands various cryptanalytic techniques more effectively than its classical counterpart. This
advancement makes it an option for securing sensitive information in today's digital world. By integrating
these enhancements, we provide a method to maintain the simplicity and historical appeal of the Vigenère
cipher while significantly improving its cryptographic strength.
keywords: : Vigenere cipher, encryption, decryption, algorithm, cryptography, cipher
Using VAR and VARX models, this study examines the links between liquidity management parameters
and the three main economic indicators in Nigeria: GDP, inflation, and unemployment. The driving force
is the crucial role that monetary policy plays in promoting economic growth and stability, especially in
developing nations like Nigeria that are dealing with issues with unemployment and inflation. Finding out
which liquidity management factors have a major impact on economic results and offering guidance for
developing effective policies are the goals. From a methodological standpoint, quarterly time series data
covering a period that includes changes in these variables are analyzed using VAR and VARX models.
The findings show that although other parameters like NIBOR and CRR have varying effects on GDP,
inflation, and unemployment, the Monetary Policy Rate (MPR) consistently affects these variables. In
order to effectively reduce economic volatility, this study's conclusion highlights the significance of
focused monetary policy interventions that are in line with economic objectives and suggests improved
policy coordination and ongoing monitoring. These results add to the body of knowledge on the efficacy
of monetary policy in Nigeria and offer useful advice to decision-makers who want to promote
sustainable economic growth.
keywords: VARX Framework, Liquidity Management, Economic Outputs, Parameters, Interaction.
The Newton-Raphson method uses the concept of iterative approximation to find a solution to a nonlinear
equation. Starting with an initial guess value for the solution, each iteration is used to refine that guess and
move it closer to the actual solution. The iterations are based on linearization around the current guess by
taking the derivative of the nonlinear equation at that point. The linear approximation is used to update the
guess by subtracting the value of the linearization from the previous guess. This process is repeated until
the exact solution is obtained. An iterative method is a mathematical procedure that is used as an initial
value to generate a sequence of improving approximate solutions for solving the non-linear equations F(x*)=0. The main purpose of this paper is to apply Newton–Raphson’s method to determine the
convergence (the approximate solution of the variables) of a non–linear infectious disease model equations
after performing some iterations with the aid of Matlab and the graph of the iterations is plotted using excel
package.
keywords: Infectious disease, Non-linear equation, Newton-Raphson Method, Convergence of a
Solution, Matlab, Microsoft Excel, Approximate solution, exact solution.
This paper investigates fully developed MHD mixed convection flow in a micro channel under the
influence of variable thermal conductivity and porous medium. The velocity slip and temperature jump at
the plates were taken in to consideration. The effects of various flow parameters entering into the problem
such as Darcy number, Hartmann number, variable thermal conductivity, mixed convection parameter,
rarefaction parameter, fluid-wall interaction parameter and wall-ambient temperature difference ratio
were discussed with the aid of line graphs. It is found that greater values of variable thermal conductivity
tend to significantly improve the temperature and velocity gradients respectively. On the hand, Darcy
number is seen to improve the fluid motion. Furthermore, when the mixed convection parameter value is
increased, the slip velocity increases on the hot wall and decreases on the cold wall.
keywords: Combined (Mixed) convection, variable thermal conductivity, Darcy number, MHD,
rarefaction, perturbation technique.
This study looks into the National Water and Sewerage Corporation's (NSWC) billing efficiency in 63
Ugandan communities. The need for NSWC to optimize revenue management and operational planning is
the driving force behind the initiative. The goal of the research is to reliably anticipate billing efficiency
based on water production, supply, and sales data using state space models, specifically SARIMAX. The
results show subtle differences in billing effectiveness between municipalities, underscoring the impact of
socioeconomic variables. To enhance decision-making, it is suggested that these elements be investigated
further and that predictive models be incorporated into NSWC's operational frameworks. In summary,
this study highlights the importance of advanced statistical techniques in utility management and helps
NSWC improve its revenue estimates and resource allocation plans.
keywords: State Space Model, Water Production, Water Supplied, Water Sold, Billing Efficiency.
