Computational and Mathematical Methods

In this study, we discuss the approximate solution of the Harry Dym nonlinear partial differential equation and its integrodifferential version. We first construct the Picard successive approximation for the equations under consideration. Then, we give a detailed calculation of the approximate solution for two cases of the partial Harry Dym integrodifferential equation. The approximate solutions are illustrated for some chosen values of the arbitrary constants. The efficiency of this semianalytical method is demonstrated through discussing the regions of the domain with small errors as well as by extracting the exact solution from the limit of the approximation.

Rabeea Mohammed Hani Darghoth

Approximate Solution of an Integrodifferential Equation Generalized by Harry Dym Equation Using the Picard Successive Method

利用Picard逐次逼近法求解Harry Dym方程推广的积分微分方程的近似解

This study delves into the often‐overlooked impact of immature mosquitoes on the dynamics of malaria transmission. By employing a mathematical model, we explore how these aquatic stages of the vector shape the spread of the disease. Our analytical findings are corroborated through numerical simulations conducted using the Runge–Kutta fourth‐order method in MATLAB. Our research highlights a critical factor in malaria epidemiology: the basic reproduction number . We demonstrate that when is below unity , the disease‐free equilibrium exhibits local asymptotic stability. Conversely, when surpasses unity , the disease‐free equilibrium becomes unstable, potentially resulting in sustained malaria transmission. Furthermore, our analysis covers equilibrium points, stability assessments, bifurcation phenomena, and sensitivity analyses. These insights shed light on essential aspects of malaria control strategies, offering valuable guidance for effective intervention measures.

Nantogmah Abdulai Sualey

Philip N. A. Akuka

Baba Seidu

Joshua Kiddy K. Asamoah

A Mathematical Analysis of the Impact of Immature Mosquitoes on the Transmission Dynamics of Malaria

不成熟蚊子对疟疾传播动力学影响的数学分析

A cell-centered finite volume semi-Lagrangian method is presented for the numerical solution of two-dimensional coupled Burgers’ problems on unstructured triangular meshes. The method combines a modified method of characteristics for the time integration and a cell-centered finite volume for the space discretization. The new method belongs to fractional-step algorithms for which the convection and the viscous parts in the coupled Burgers’ problems are treated separately. The crucial step of interpolation in the convection step is performed using two local procedures accounting for the element where the departure point is located. The resulting semidiscretized system is then solved using a third-order explicit Runge-Kutta scheme. In contrast to the Eulerian-based methods, we apply the new method for each time step along the characteristic curves instead of the time direction. The performance of the current method is verified using different examples for coupled Burgers’ problems with known analytical solutions. We also apply the method for simulation of an example of coupled Burgers’ flows in a complex geometry. In these test problems, the new cell-centered finite volume semi-Lagrangian method demonstrates its ability to accurately resolve the two-dimensional coupled Burgers’ problems.

Ilham Asmouh

Mofdi El-Amrani

Mohammed Seaid

Naji Yebari

A Cell-Centered Semi-Lagrangian Finite Volume Method for Solving Two-Dimensional Coupled Burgers’ Equations

一种求解二维耦合Burgers方程的基于单元中心的半拉格朗日有限体积方法

Mathematical models play an important role in epidemiology. The inclusion of a spatial component in epidemiological models is especially important to understand and address many relevant ecological and public health questions, e.g., when wanting to differentiate transmission patterns across geographical regions or when considering spatially heterogeneous intervention measures. However, the introduction of spatial effects can have significant consequences on the observed model dynamics and hence must be carefully analyzed and interpreted. Cellular automata epidemiological models typically rely on simplified computational grids but can provide valuable insight into the spatial dynamics of transmission within a population by suitably accounting for the connections between individuals in the considered community. In this paper, we describe a stochastic cellular automata disease model based on an extension of the traditional Susceptible-Infected-Recovered (SIR) compartmentalization of the population, namely, the Susceptible-Hospitalized-Asymptomatic-Recovered (SHAR) formulation, in which infected individuals either present a severe form of the disease, thus requiring hospitalization, or belong to the so-called mild/asymptomatic class. The critical transmission threshold is derived analytically in the nonspatial SHAR formulation, and this generalizes previously obtained theoretical results for the SIR model. We present simulation results discussing the effect of key model parameters and of spatial correlations on model outputs and propose an algorithm for tracking the evolution of infection clusters within the considered population. Focusing on the role of import and criticality on the overall dynamics, we conclude that the current spatial setting increases the critical transmission threshold in comparison to the nonspatial model.

Damián Knopoff

Nicole Cusimano

Nico Stollenwerk

Maíra Aguiar

Spatially Extended SHAR Epidemiological Framework of Infectious Disease Transmission

传染病传播的空间扩展SHAR流行病学框架

In December 2019, a severe respiratory syndrome (COVID-19) caused by a new coronavirus (SARS-CoV-2) was identified in China and spread rapidly around the globe. COVID-19 was declared a pandemic by the World Health Organization (WHO) in March 2020. With eventually substantial global underestimation, more than 225 million cases were confirmed by the end of August 2021, counting more than 4.5 million deaths. COVID-19 symptoms range from mild (or no symptoms) to severe illness, with disease severity and death occurring according to a hierarchy of risks, with age and preexisting health conditions enhancing the risks of disease severity manifestation. In this paper, a mathematical model for COVID-19 transmission is proposed and analyzed. The model stratifies the studied population into two groups, older and younger. Applied to the COVID-19 outbreaks in Spain and in Italy, we find the disease-free equilibrium and the basic reproduction number for each case study. A sensitivity analysis to identify the key parameters which influence the basic reproduction number, and hence regulate the transmission dynamics of COVID-19, is also performed. Finally, the model is extended to its stochastic counterpart to encapsulate the variation or uncertainty found in the transmissibility of the disease. We observe the variability of the infectious population finding its distribution at a given time, demonstrating that for small populations, stochasticity will play an important role.

Akhil Kumar Srivastav

Deterministic and Stochastic Dynamics of COVID-19: The Case Study of Italy and Spain

COVID-19的确定性和随机动力学：意大利和西班牙的案例研究

In various fields, such as economics, finance, bioinformatics, geology, and medicine, namely, in the cases of electroencephalogram, electrocardiogram, and biotechnology, cluster analysis of time series is necessary. The first step in cluster applications is to establish a similarity/dissimilarity coefficient between time series. This article introduces an extension of the affinity coefficient for the autoregressive expansions of the invertible autoregressive moving average models to measure their similarity between them. An application of the affinity coefficient between time series was developed and implemented in R. Cluster analysis is performed with the corresponding distance for the estimated simulated autoregressive moving average of order one. The primary findings indicate that processes with similar forecast functions are grouped (in the same cluster) as expected concerning the affinity coefficient. It was also possible to conclude that this affinity coefficient is very sensitive to the behavior changes of the forecast functions: processes with small different forecast functions appear to be well separated in different clusters. Moreover, if the two processes have at least an infinite number of π - weights with a symmetric signal, the affinity value is also symmetric.

Ana Paula Nascimento

Alexandra Oliveira

Brígida Mónica Faria

Rui Pimenta

Mónica Vieira

Cristina Prudêncio

Helena Bacelar-Nicolau

Affinity Coefficient for Clustering Autoregressive Moving Average Models

聚类自回归移动平均模型的亲和系数

In this work, we suggest a new numerical scheme called the fractional higher order Taylor method (FHOTM) to solve fractional differential equations (FDEs). Using the generalized Taylor’s theorem is the fundamental concept of this approach. Then, the local truncation error generated by the suggested FHOTM is estimated by proving suitable theoretical results. At last, several numerical applications are given to demonstrate the applicability of the suggested approach in relation to their exact solutions.

Iqbal M. Batiha

Iqbal H. Jebril

Amira Abdelnebi

Zoubir Dahmani

Shawkat Alkhazaleh

Nidal Anakira

A New Fractional Representation of the Higher Order Taylor Scheme

高阶泰勒方案的新分数表示

This article proposes a collocation approach based on a redefined quintic B-spline basis for solving the time-fractional Whitham-Broer-Kaup equations. The presented method involves discretizing the time-fractional derivatives using an <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msub></math> -approximation scheme and then approximating the spatial derivatives using the redefined quintic B-spline basis. The von Neumann technique has been used to demonstrate that the proposed method is unconditionally stable. The error estimates are discussed and show that the proposed method is third-order convergent. The results demonstrate the potential of the proposed method as a reliable tool for solving fractional differential equations.

Adel R. Hadhoud

Abdulqawi A. M. Rageh

Redefined Quintic B-Spline Collocation Method to Solve the Time-Fractional Whitham-Broer-Kaup Equations

重定义五次B样条配置法求解时间分数阶Whitham-Broer-Kaup方程

In this study, we present a mathematical model for the codynamics of taeniasis and neurocysticercosis and rigorously analyze it. To understand the underlying dynamics of the proposed model, basic system properties such as the positivity and boundedness of solutions are investigated through the completing differential process. The basic reproduction number was calculated using the next-generation matrix method, and the analysis showed that when <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"><msub><mrow><mi mathvariant="script">R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>&lt;</mo><mn>1</mn></math> , the disease in the community eventually dies out, and when <math xmlns="http://www.w3.org/1998/Math/MathML" id="M2"><msub><mrow><mi mathvariant="script">R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>&gt;</mo><mn>1</mn></math> , the diseases persist. Local stability of the equilibria was analyzed using the Jacobian matrix, and Lyapunov function techniques were used to determine the global analysis, which showed that the endemic equilibrium point was globally stable when <math xmlns="http://www.w3.org/1998/Math/MathML" id="M3"><msub><mrow><mi mathvariant="script">R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>&gt;</mo><mn>1</mn></math> . On the other hand, the disease-free equilibrium was determined to be globally stable when <math xmlns="http://www.w3.org/1998/Math/MathML" id="M4"><msub><mrow><mi mathvariant="script">R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>&lt;</mo><mn>1</mn></math> . To identify the most influential parameters of the proposed model, partial correlation coefficient techniques were used. The numerical results depict that the model aligns well with the transmission dynamics, which goes through two populations: humans and pigs, whereby the model system stabilizes after some time, showing the validity of the proposed model. Furthermore, the simulations of the proposed model revealed that the shedding habit of infected humans with taeniasis and the bad cooking habit or eating of raw or undercooked pork products have a higher impact on the spread of neurocysticercosis and taeniasis in the community. Hence, this study proposes that in order to control taeniasis and neurocysticercosis, effective disease control measures should primarily prioritize hygienic behaviour and proper cooking of pork meat to the required temperature.

Gideon Eustace Rwabona

Verdiana Grace Masanja

Sayoki Mfinanga

Abdoelnaser Degoot

Silas Mirau

A Mathematical Model for Transmission of Taeniasis and Neurocysticercosis

带绦虫病和囊虫病传播的数学模型

In this study, Secant Kumaraswamy family of distributions is proposed and studied. This is motivated by the fact that no one distribution can model all types of data from different fields. Therefore, there is the need to develop distributions with desirable properties and flexible enough for modelling data exhibiting different characteristics. Some properties of the new family of distributions, including the quantile function, moments, moment generating function, and mean residual life function, are derived. Five special cases of the family of distributions are presented, and their flexibility is shown by the varying degrees of skewness and kurtosis and nonmonotonic hazard rates. The maximum likelihood estimation method is used to obtain estimators of the family of distributions. Two location-scale regression models are developed for the Secant Kumaraswamy Weibull distribution, which is a special case of the family of distributions. Six different real datasets are used to demonstrate the usefulness of the family of distributions and the regression models. The results show that the family of distributions can be used to model real datasets.

Salifu Nanga

Shei Baba Sayibu

Irene Dekomwine Angbing

Mubarika Alhassan

Abdul-Majeed Benson

Abdul Ghaniyyu Abubakari

Suleman Nasiru

Secant Kumaraswamy Family of Distributions: Properties, Regression Model, and Applications

割线Kumaraswamy分布族：性质、回归模型及应用

Abbreviation
Journal Impact	0.80
Quartiles(Global)	MATHEMATICS, APPLIED(Q3)

ISSN	2577-7408
h-index	11

Publication Information	Publisher: Wiley-Blackwell Publishing Ltd，Publishing cycle: ，Journal Type: journal，Open Access Journals: Yes
Basic data	Year of publication: 2019，Proportion of original research papers: 100.00%，Self Citation Rate:， Gold OA Rate: 49.71%
Journal Fees	$800Details
Average review cycle	19 weeks

Computational and Mathematical Methods

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