Mathematical Modeling and Numerical Analysis

This paper analyzes the 2-point Fractional Block Method based on the Backward Differentiation Formula for solving stiff fractional-order differential equations. An analysis of the stability properties of the method is conducted to verify its A-stability. Since the method fulfills the characteristic, it can be employed to approximate solutions for stiff problems. Consequently, two test problems are solved to assess the method’s performance. As a result, the derived method exhibits advantages over existing methods in terms of accuracy.

This paper presents an efficient approach for determining an approximate solution of system of first order differential equations with variable coefficients. It is introduced as a differential equation with piecewise constant arguments corresponding to the considered initial value problem, which depend on a positive integer number n. It is proved that this equation has a unique piecewise-smooth solution, which will be an approximate solution for the considered initial value problem for large n. Numerical results are given on examples showing the efficiency and high accuracy of the suggested method.

The global COVID-19 pandemic has underscored the importance of understanding and managing infectious disease dynamics. This paper focuses on the numerical solution of the Susceptible-Infectious-Recovered (SIR) model, a widely used mathematical framework for studying disease transmission. The numerical solution is implemented through the Adams–Bashforth method, known for its efficiency in solving ordinary differential equations. The project incorporates the element of vaccination into the classical SIR model to explore the impact of vaccination campaigns on disease dynamics. This project contributes to the ongoing efforts to understand and mitigate the effects of COVID-19 by offering a computational perspective on disease dynamics and vaccination strategies. The combined utilization of the Adams–Bashforth and RK4 methods enhances the accuracy and efficiency of the numerical solution, making it a valuable tool for researchers and policymakers alike in addressing the challenges posed by infectious diseases. The results analysis shows that the vaccinated model outperformed the unvaccinated model, with fewer estimated infections in general, indicating that the Adams–Bashforth method is efficient in approximating the further behavior of vaccine and number of infected people interaction.

This study evaluates the performance of advanced numerical techniques based on the block backward differentiation formula (BBDF) in solving therapy models for Chronic Lymphocytic Leukemia (CLL). The CLL treatment model uses deferential equations to illustrate the interactions between cancer cells and treatment. The approximation uses BBDF-based model known as diagonal implicit BBDF with intermediate points to capture the dynamic interactions between cancer cells, immune cells, and therapeutic agents. The effectiveness of the new solver is assessed by comparing its results with both analytical solutions and existing solver. The findings demonstrate that the new method is effective for solving CLL therapy models.

Tuberculosis (TB) is a highly infectious disease caused by Mycobacterium tuberculosis (MTB) that primarily affects the lungs. It spreads through the air when infected individuals cough, sneeze, or spit. TB remains a significant global health problem, including in Malaysia, where it poses substantial challenges. This study formulates a deterministic model of TB incorporating vaccination to study the dynamics of TB. The model is based on the susceptible-vaccinated-infectious-recovered (SVIR) framework. The disease-free equilibrium (DFE) point is identified, and the basic reproduction number \(R_0\) is computed. The stability result shows that the DFE is stable when \(R_0\) is less than 1 (\(R_0 < 1\)), indicating that TB will not persist in the population long term. Additionally, we analyse the effectiveness of the BCG vaccine by examining two models: one with and one without vaccination. The model without vaccination shows an increasing number of infected individuals, while the vaccinated model yields different results. This comparison underlines the essential role of immunisation in TB infection control. By understanding the stability of the DFE and assessing the vaccine’s effectiveness, we provide valuable insights for TB control efforts and inform public health authorities of strategies to combat the virus.

This paper represents an efficient approach for solving approximated solution of the second-order nonlinear systems of differential equations using piecewise constant argument methods. A system of differential equations with piecewise constant arguments that depends on a positive integer n is introduced. It is proved that this system of equations has a unique piecewise solution, which is an approximate solution to the considered initial value problem for large n. Numerical results are presented on examples that demonstrate the effectiveness and high accuracy of the proposed method.

This study addresses the problem of limited research on the performance efficiency of Malaysian airports, with most studies focusing on airports of other countries. To initiate such performances analysis, this study aims to fill this gap by employing Data Envelopment Analysis (DEA) model to calculate the relative efficiency of Malaysian international airports and determine the ideal value of inputs and outputs to maximize the performance of the inefficient airports. DEA is a mathematical performance measure technique that can evaluate the relative efficiency of decision-making units (DMUs). The DMU in this study are eight selected Malaysian international airports. The input data are the number of runways, runway length, check-in counters, boarding gates, while the output data are passenger movement and aircraft movement. The result has revealed varying levels of relative efficiency among the airports, with DMU1, DMU7, and DMU8 achieving the highest efficiency scores. The findings suggest rooms for improvement for other five international airports. Improvement strategies were assessed by adjusting factors of input and output values. By implementing the proposed improvement strategies, the relative efficiency level of the DMU have increased significantly. This study provides valuable insights for airport authorities to enhance operational efficiency, contributing to the development and improvement of Malaysian international airports.

In decision-making and modeling uncertainty, fuzzy numbers have been extensively used due to their ability to represent imprecision and vagueness. However, in many real-world applications, decision-makers (DMs) face not only uncertainty but also degrees of indeterminacy and inconsistency that fuzzy numbers may not adequately capture. This study employs interval neutrosophic sets (INS), an extension of neutrosophic sets, to provide a more comprehensive framework for addressing such situations by incorporating truth, indeterminacy, and falsity values into the decision-making method known as Measurement of Alternatives and Ranking according to Compromise Solution (MARCOS). The proposed model is applied to examine learning success criteria in an open distance learning (ODL) environment. The study aims to investigate success criteria for learning and the type of e-learning systems that contribute to successful learning outcomes in online distance education. Specifically, it seeks to identify the criteria and alternatives that best support success in ODL using the interval neutrosophic MARCOS method. The selection of the best criteria for ODL success is based on six criteria: student characteristics, instructor characteristics, learning environment, instructional design, information technology, and the level of collaboration. The results of this study confirm that asynchronous learning is the most effective system for open distance learners. Furthermore, it is recommended as the optimal method, particularly for those seeking the best option for success in ODL.

A veterinary clinic is a medical facility that treats sick or wounded animals. Many veterinary clinics have been set up in Malaysia to assist animal enthusiasts in treating their pets. Regular check-ups for pets, emergency, and urgent treatment, as well as boarding and grooming, are all available at the clinic. Many of the services need many staff to handle. Thus, to manage many staff and ensure that each position is well assigned, a good workforce schedule must be created. Therefore, this study modified a Binary Programming (BP) model to represent the real-life problem of workforce scheduling for a veterinary clinic. The study aimed to minimize the weekly number of staff in any working shifts to produce the optimal schedule in the veterinary clinic. This weekly schedule is created to determine the task for each staff shift, while considering the rest day in between working shifts, the minimum number of employees for each shift, among other consideration. This paper focused on two sub-case studies, and they are based on the data collected from a local veterinary clinic. The modified BP model was then solved using Open Solver software. To determine the best working schedule of veterinary staff, the results obtained by the two case studies were compared based on the shortcomings. The findings indicate that the new model could be used to offer a flexible working schedule that is both reliable and effective; however, there are also some rooms for improvement.

The Susceptible-Exposed-Infectious-Recovered (SEIR) model serves as a pivotal tool in simulating infectious diseases like COVID-19, offering a structured framework to analyze how diseases spread through populations over time. It allows researchers and policymakers to estimate key epidemiological parameters such as transmission rates, incubation periods, and recovery rates, crucial for designing effective public health interventions. This study implements multistep block method with predictor and corrector scheme to approximate the population representing individuals who are susceptible to the disease, those that exposed to the disease, those who has infected, and also those who has recovered from the disease. The multistep method is derived by using Lagrange interpolation and the two-points solutions are obtained simultaneously in block method. These two solutions are then iterated by using predictor-corrector scheme to improve the accuracy of the approximate solutions. The proposed method then tested to solve the SEIR model and compared with the established previous methods to observe its accuracy performance. The factors contributed to its computational time required such as total steps and total function calls also discussed and compared with previous method. Overall, the research contributes a robust computational framework for SEIR modeling, advancing capabilities to simulate and understand disease spread dynamics effectively.

Simulating weather data helps researchers predict climate patterns and analyze the transmission dynamics of vector-borne diseases. A simulation study was conducted to evaluate the model performance of Bayesian Poisson Generalized Linear Mixed Model (GLMM) using simulated data to predict the dengue incidence in Selangor. At first, the actual dengue data was collected from the Ministry of Health Malaysia, and weather data (temperature, relative humidity and rainfall) was obtained from online climate data. The simulation study began by generating daily temperature and relative humidity using ARIMA model, followed by daily rainfall using a probability distribution. In total, 16,425 data observations were simulated throughout nine districts. The study revealed that the simulated daily temperature appears to be closely matched to the actual data. Nevertheless, the simulated daily relative humidity and rainfall resulted in variability across districts. It was found that a 1% increase in relative humidity raises dengue incidence by 0.19% daily, with increases of 0.19%, 0.22%, 0.21%, and 0.17% at lags of 7, 14, 21, and 28 days, respectively. Similarly, a 1 mm increase in rainfall raises dengue incidence by 0.11% daily, with increases of 0.11%, 0.12%, 0.11%, and 0.12% at the same lags. In addition, the Bayesian model fitted in the study captured a weak spatial autocorrelation (0.0480) and a very strong temporal autocorrelation (0.9996) in the simulated dataset generated earlier. Additional weather variables and random effects can be considered in model formulation to improve the accuracy of the simulation model in future.

Traditional statistical distributions often struggle with modeling asymmetric or extreme data, particularly when data is heavily skewed or concentrated in one tail. Classical distributions like the normal or exponential distributions fail to provide accurate representations in such cases, leading to poor model fitting and inadequate predictions. This issue is especially evident in applications involving survival analysis, insurance, and extreme value modeling, where the data exhibit irregular patterns that require more flexible distribution families. To address these limitations, this study proposes a new probability distribution, the Hybrid Odd Lomax Fréchet (HOLFr), according to the Odd Lomax family, which is a model for a new probability distribution consisting of four parameters, which introduces greater flexibility and accuracy in modeling real-world data with extreme characteristics. The new distribution expands upon the Odd Lomax family by incorporating additional parameters, allowing it to better handle skewness and kurtosis in complex datasets. In addition, the study will present a number of statistical properties of the hybrid distribution such as the moment generating function, survival function, risk function, Quintile function, pdf expansion, ordered statistics as well as other statistical properties that represent a few of the many mathematical and statistical features of the hybrid distribution. The parameters of the two models were also estimated using the maximum likelihood function. In order to obtain a distribution that is highly flexible to accommodate different types of real data, a Monte Carlo simulation was conducted to demonstrate the efficiency of estimating the unknown parameters of the new distribution using the maximum likelihood method. The proposed HOLFr distribution demonstrated significant flexibility and robustness in modeling asymmetric and extreme data. Through Monte Carlo simulations and real-world applications, the new distribution was compared against established models, showing superior performance in terms of flexibility and goodness-of-fit criteria such as AIC, BIC, CAIC, and HQIC. The results highlight the effectiveness of HOLFr in fitting both positively and negatively skewed data, making it a valuable tool for survival analysis and other areas requiring robust statistical models. The HOLFr distribution is a promising extension that offers enhanced accuracy in real-world data modeling, as demonstrated by its application to survival data.

The optimal itinerary offers higher efficiency and is very crucial, especially for an individual with a restricted amount of time to visit their point of interest. The Miller-Tucker-Zemlin Traveling Salesman Problem (MTZ-TSP) is an approach that finds the shortest path that visits multiple vertices using integer linear programming technique. Utilizing the MTZ-TSP in the context of travel itinerary creation could improve travel experience in an area, especially for solo traveler. Islamic landmarks refer to places, sites, or landmarks that hold significance within the Islamic faith or culture. However, the study that used MTZ-TSP to develop travel itineraries for solo travelers with limited time, focusing on enhancing the travel experience associated with Islamic landmarks in urban area, is still lacking. Hence, this paper presents an optimized travel itinerary for visiting seven Islamic landmarks in the selected urban area, namely, Kuala Lumpur, Malaysia, using the MTZ-TSP approach. Three initial start points were selected to provide a diverse range of travel itineraries for tourists. As a result, it was found that the total travel time to traverse all of the selected Islamic landmarks would be 98 min.

Water conservation is becoming a bigger challenge globally as the demand for water increases. Water losses are a concern for water supply service systems worldwide, particularly in developing nations. As a result, the problem of water losses, also identified as Non-Revenue Water (NRW), has become crucial to the administration of the water supply service. The current policy of the efficiency measurement by the service providers is impractical since NRW has been ignored as the undesirable product in the water supply system. Previously, there are many studies on measuring the efficiency of the water providers by using Data Envelopment Analysis (DEA). However, conventional DEA does not consider the undesirable output in efficiency measurement. The measurement model without the presence of undesirable outputs will have an unfair inaccurate result. Thus, Scale Directional Distance Function (SDDF) model will be applied in this study as an extension to the conventional DEA approach in measuring the efficiency of water supply providers of 14 states in Malaysia. The result displays that seven states which are Johor, Melaka, Pulau Pinang, Perak Perlis, Sabah, and Selangor achieved full efficiency score and the average efficiency score is 82.39%. In addition, this approach is able to establish target values for decreasing or extension of the outputs to make future improvements as well as to achieve full efficiency.

Managing the freshness of postharvest vegetables in the supply chain poses significant challenges. Freshness, a critical quality indicator, directly impacts the fitness for consumption and consumer purchasing decisions. Previous studies have identified various factors influencing vegetables’ freshness, including consumer perspectives, physiological characteristics, temperature management, and delivery time. However, limited research compares the factors across different stakeholders in the supply chain. This study aims to identify influential factors affecting vegetables’ freshness from the perspectives of producers, wholesalers, retailers, and transport providers. A stratified sampling survey was conducted with 151 respondents to identify key freshness determinants. Multiple linear regression analyses revealed that mode of transportation, delivery time, biological control, and temperature control significantly influence postharvest vegetable freshness. These factors were utilized to formulate a freshness score, an objective function for optimizing vehicle routing in vegetable distribution. The findings underscore the importance of integrating these criteria into supply chain practices to enhance freshness, reduce losses, and improve efficiency. Strategies proposed include best practices for postharvest storage and handling to preserve quality, extend shelf life, and minimize waste. To ensure efficient supply chain operations and higher consumer satisfaction, stakeholders must prioritize these critical factors. This research provides valuable insights into optimizing the fresh vegetable supply chain, contributing to improved sustainability and resilience.

The study examines the relationship between the impact severity of road accidents and the spatial grouping of Malaysian states during the COVID-19 pandemic in 2020 and 2021, addressing the lack of analysis on these trends in Malaysia. The road accidents impact severity is divided into two subgroups, which are injury severity level (i.e., death, bad injury, and light injury) and accident severity category (i.e., fatal, serious, and minor accidents). Nine combinations of these severity levels and categories for each observed year are analyzed using linear regression analysis. The significance and correlation for each combination is observed and studied. Further analysis is performed using quadrant analysis, grouping states based on the mean-centered positions. Subsequently, chi-square analysis is applied to these quadrant-based groups to explore associations between the spatial distribution of states and the combinations of severity levels and categories. The study aims to explore the spatial trends of road accidents in Malaysia, highlighting how accident and injury severities are distributed across different states during the pandemic. The findings showed that only the accident severity categories directly linked to the injury severity level have a strong linear relationship, regardless of the year. Pulau Pinang demonstrated a worsening trend, shifting from Quadrant III in 2020 to Quadrant I in 2021 across all combinations, while Selangor remained in Quadrant I for all cases throughout the pandemic. The impact severity for death and serious accident, as well as for bad injury and fatal accident, showed no significant relationships between the years 2020 and 2021.

In three-dimensional Euclidean space, Alexandrov solved the problem of recovering a convex surface from a given extrinsic curvature of the vertices in the class of convex polyhedra and generalized it for the class of convex surfaces. The purpose of this article is to solve an analogue problem in semi-hyperbolic space. First we interpret the semi-hyperbolic space inside the sphere of isotropic space. Let us prove that convex surfaces of semi-hyperbolic space are represented by convex surfaces contained within the sphere of isotropic space. The sphere of isotropic space is a cylinder with rectilinear generatrices. Moreover, bounded convex surfaces in semi-hyperbolic space are expressed by convex surfaces strictly containing inside a sphere of isotropic space, and infinite surfaces using surfaces that have common points with a cylinder, that is, a sphere of isotropic space. For convex surfaces in semi-hyperbolic space, the extrinsic curvature is determined as a positive definite, additive function of the Borel set. A theorem for the existence and uniqueness of a surface with a given function of extrinsic curvature is proven which is equivalent to the existence and uniqueness of a solution to the Monge–Ampere equation.

This work aims to enhance several mathematical concepts within fuzzy bitopological spaces by analyzing various fuzzy separation axioms, such as \(T_h\) and \(T_{hw}\), where \(h={0,1,2,{2_\frac{1}{2}}}\). The study employs different types of fuzzy generalized closed sets of \((X,\delta _i,\delta _j)\), including fuzzy \((i,j)-g\alpha \)-closed sets, fuzzy \((i,j)-gp\)-closed sets, fuzzy \((i,j)-gs\)-closed sets, and fuzzy \((i,j)-g\beta \)-closed sets, with \(i,j=\{1,2\}\) and \(i\ne j\). After that, we give some important theorems that explain how they relate to each other and what their main characteristics are. These are followed by some strong counterexamples that show the inverse connection is not valid. This study’s conclusions are novel to the domain of fuzzy bitopological spaces. Furthermore, this work will serve as a valuable reference by introducing numerous fundamental concepts that remain unexplored.