Fractional derivative models for the spread of diseases

This thesis considers the mathematical modelling of disease, using fractional differential equations in order to provide a tool for the description of memory effects. In Chapter 3 we illustrate a commensurate fractional order tumor model, and we find a critical value of the fractional derivative dependent on the parameter values of the model. For fractional derivatives of orders less than the critical value an unstable equilibrium point of the system becomes stable. In order to show changes in the observed areas of attraction of two stable points in the system, we then consider a fractional order SIR epidemic model and investigate the change from a monostable to a bistable system.;Chapter 4 considers a model for virus dynamics where the fractional orders for populations are different, called an incommensurate system. An approximate analytical solution for the characteristic equation of the incommensurate model is found when the different fractional orders are similar and close to the critical value of the fractional order of the commensurate system. In addition, the instability boundary is found as a function of both parameters. A comparison between analytical and numerical results shows the high accuracy of this approximation.;Chapter 5 consists of two parts, in the first part we generalise the integer Fisher's equation to be a space-time fractional differential equation and consider travelling wave solutions. In the second part we generalise an integer SIR model with spatial heterogeneity, which was studied by Murray [117], to a space-time fractional derivative model. We apply the (G0/G)-expansion method and find travelling wave solutions, although in this case we must consider the Jumarie's modified Riemann-Liouville fractional derivative. Finally, we consider the effect of changing the orders of time and space fractional derivatives on the location and speed of the travelling wave solution.This thesis considers the mathematical modelling of disease, using fractional differential equations in order to provide a tool for the description of memory effects. In Chapter 3 we illustrate a commensurate fractional order tumor model, and we find a critical value of the fractional derivative dependent on the parameter values of the model. For fractional derivatives of orders less than the critical value an unstable equilibrium point of the system becomes stable. In order to show changes in the observed areas of attraction of two stable points in the system, we then consider a fractional order SIR epidemic model and investigate the change from a monostable to a bistable system.;Chapter 4 considers a model for virus dynamics where the fractional orders for populations are different, called an incommensurate system. An approximate analytical solution for the characteristic equation of the incommensurate model is found when the different fractional orders are similar and close to the critical value of the fractional order of the commensurate system. In addition, the instability boundary is found as a function of both parameters. A comparison between analytical and numerical results shows the high accuracy of this approximation.;Chapter 5 consists of two parts, in the first part we generalise the integer Fisher's equation to be a space-time fractional differential equation and consider travelling wave solutions. In the second part we generalise an integer SIR model with spatial heterogeneity, which was studied by Murray [117], to a space-time fractional derivative model. We apply the (G0/G)-expansion method and find travelling wave solutions, although in this case we must consider the Jumarie's modified Riemann-Liouville fractional derivative. Finally, we consider the effect of changing the orders of time and space fractional derivatives on the location and speed of the travelling wave solution

Approximate Solutions for Fractional Gas Dynamics and Convection-Diffusion Equations via the Temimi-Ansari Method

In this paper, a new analytical iterative method is used to obtain the fractional analytical solutions of the nonlinear gas dynamics and convectiondiffusion equations. The paper’s novelty appears in its specific application of the Caputo fractional operator to conventional equations while achieving highly accurate solutions. Numerical outcomes for various cases of the equations are represented via tables and graphs. The convergence analysis for the present approach was completed. The methodology is very capable of reducing the size of the analytical steps and is convenient and efficient for solving nonlinear fractional equations. The Temimi-Ansari method’s applicability across different types of fractional differential equations indicates its potential as a powerful tool in solving nonlinear fractional models in diverse scientific and technical fields.OPEN ACCESS Received: 19/07/2024 Accepted: 11/11/2024 Published: 07/04/202

A Fractional Semi-Analytical Iterative Method for the Approximate Treatment of Fisher’s Equations

This study presents a novel fractional semi-analytical iterative approach for solving nonlinear fractional Fisher’s equations using the Caputo fractional operator. The primary objective is to provide a method that yields exact solutions to nonlinear fractional equations without requiring assumptions about nonlinear terms. By applying the Temimi-Ansari Method (TAM) with fractional calculus, this approach offers a robust solution to the time-fractional nonlinear Fisher’s equation, a model relevant in fields such as population dynamics, tumor growth, and gene propagation. In this work, tables and graphical illustrations show that the proposed method minimizes computational complexity and delivers significant accuracy across multiple cases of Fisher’s equations. The findings indicate that TAM with fractional order derivatives provides accurate, efficient approximations with reduced computational workload, showcasing the technique’s potential for addressing a wide range of nonlinear fractional differential equations.OPEN ACCESS Received: 19/07/2024 Accepted: 01/11/202

Association of Women Empowerment with Intimate Partner Violence in Saudi Arabia

Mostafa A Abolfotouh,1– 3 Maha Almuneef2,4 1Research Training Academy, King Abdullah International Medical Research Center, Riyadh, Saudi Arabia; 2King Saud Bin-Abdulaziz University for Health Sciences, Ministry of National Guard-Health Affairs, Riyadh, Saudi Arabia; 3Department of Family Health, High Institute of Public Health, Alexandria University, Alexandria, Egypt; 4Department of Pediatrics, King Abdullah Specialized Children Hospital, Ministry of National Guard-Health Affairs, Riyadh, Saudi ArabiaCorrespondence: Mostafa A Abolfotouh, FASHA (USA), Professor and Senior Research Scientist, Research Training & Development Section, King Abdullah International Medical Research Center (Mail Code 1515)/King Saud Bin-Abdulaziz University for Health Sciences (KSAU-HS)/King Abdulaziz Medical City, Ministry of National Guard-Health Affairs, POB 22490, Riyadh, 11426, Saudi Arabia, Email [email protected]: The prevalence of intimate partner violence (IPV) is higher among women with lower social and economic status. Moreover, empowerment-focused interventions might not protect them from domestic abuse. This study assessed Saudi women’s empowerment and its usefulness as a stand-alone IPV predictor.Methods: 400 married women, ages 19 to 65, who visited the outpatient clinics of PHC centers in Riyadh were interviewed using the Women’s Empowerment module and the previously Arabic-validated version of the WHO multi-country instrument on Violence Against Women (VAW) to learn more about the beliefs of women regarding IPV and women’s empowerment (in the decision-making process and the freedom to move). Logistic regression analysis was employed to identify the IPV predictors. At p< 0.05, significance was established.Results: In terms of physical (18.5%), emotional (25.5%), sexual (19.2%), and economic (25.3%) violence, the lifetime overall IPV prevalence was 44.8%. 19.5% of all women said they had a negative attitude towards IPV. From 41.8% of women who reported a positive attitude towards violence to 45% and 56.8% among those who reported neutral and negative attitudes, respectively, the prevalence of IPV rose significantly (χ 2LT = 4.35, p = 0.037). Roughly one-third of women had no authority to make decisions (33%) or the freedom to move about (40.1%). When comparing empowered to non-empowered women, it was found that IPV was significantly less common in the decision-making process (30.1% versus 77%, χ 2=74.91, p< 0.001) and in the freedom to move (16.2% versus 27.7%, χ 2=5.77, p=0.016). After adjusting for relevant confounders, women’s empowerment was an independent predictor of IPV (OR=0.734, 95% CI: 0.63– 0.85).Conclusion: Women’s empowerment is a strong predictor of IPV. Women who lack social and economic authority should receive assistance from the government. Advocacy initiatives that emphasize transforming cultural perceptions of violence and enabling women to participate in decision-making processes should be supported.Keywords: Saudi Vision 2030, violence against women, women’s health, interspousal violence, women’s rights, women’s abuse, child abuse and neglec

The Relationship between Gram-Negative Colonisation and Bloodstream Infections in Neonates: A Systematic Review and Meta-Analysis.

OBJECTIVES: Neonates admitted to Neonatal Intensive Care Units (NICU) are at significant risk of developing bloodstream infections (BSIs). Gram-negative bacteria (GNB) both colonise and infect, but the association between these entities is unclear. By conducting a systematic literature review, we aimed to explore the impact of factors on the association between GN colonisation and GN-BSI at both baby level and unit level. METHODS: We searched Medline, Embase, and Cochrane Library. Observational cohort studies published after 2000 up to June 2016 reporting data on the total number of neonates (0-28 days) colonised with GNB assessed by rectal/skin swab culture and the total number of neonates with GN-BSI (same bacteria) were included. Studies were excluded if data on skin/rectal colonisation, neonates, and GNB could not been identified separately. The meta-analyses along with multivariate meta-regression with random-effect model were performed to investigate factors associated with the GN colonisation and GN-BSI at baby-level and unit-level. RESULTS: 27 studies fulfilled our inclusion criteria, 15 for the baby-level and 12 for the unit-level analysis. Study heterogeneity was high, with suboptimal overall quality of reporting assessed by the STROBE-NI statement (44.8% of items adequately reported). In 1,984 colonised neonates, 157 (7.9%) developed GN-BSI compared with 85 of 3,583 (2.4%) non-colonised neonates. Considerable heterogeneity across studies was observed. Four factors were included in the meta-regression model: Gross domestic product (GDP), pathogen, outbreak, and frequency of screening. There was no statistically significant impact of these factors on GN colonisation and GN-BSI in baby level. We were unable to perform the multivariate meta-regression due to the insufficient reported data for unit level. CONCLUSIONS: Study limitations include the small number and the high heterogeneity of the included studies. While this report shows a correlation between colonisation and BSI risk, this data currently doesn't support routinely screening for GNB. The analysis of large cohorts of colonised neonates with clinical outcomes is still needed to define the major determinants leading from colonisation to infection

Child Maltreatment Prevention Readiness Assessment in Oman

Objectives: This study aimed to evaluate Oman’s readiness for implementing large-scale child maltreatment prevention (CMP) programmes. Methods: This cross-sectional study was conducted between May and August 2016 in Oman. Participants, referred to as key informants, were individuals with influence and decision-making powers over CMP. The multidimensional Readiness Assessment for the Prevention of Child Maltreatment tool, developed by the World Health Organization with the help of collaborators from middle- and low-income countries, was used to assess 10 dimensions of readiness, each with a maximum score of 10. Results: A total of 49 participants were included in this study (response rate = 98%). The mean total score for the 10 dimensions was 50.17 out of 100 possible points. The participants showed high mean readiness scores on legislation, mandates and policies (9.08) followed by knowledge of CMP (7.55), institutional resources and links (6.12), willingness to address the problem (5.35), informal social resources (5.15) and current programme implementation and evaluation (5.10). Participants had low scores in readiness in association with human and technical resources (2.44), attitudes towards CMP (2.90), scientific data on CMP (3.06) and material resources (3.46). Conclusion: The results of this study indicate that Oman has a moderate level of readiness to implement largescale evidence-based prevention programmes against child maltreatment; however, several dimensions still need to be strengthened. It is important to develop a national strategy that outlines a framework for organising and prioritising efforts towards CMP.Keywords: Child Maltreatment; Program Development; Attitude; World Health Organization; Oman

The Laplace Residual Power Series Method for Solving Fractional Fifth-Order Korteweg–de Vries Equations

This study explores a modern analytical approach for solving the fractional fifth-order Korteweg&ndash;de Vries (KdV) equations, which describe intricate wave phenomena influenced by nonlinearity, dispersion, and memory effects. Specifically, the Laplace residual power series method (LRPSM) is utilized to obtain accurate approximate analytical solutions for three fundamental fractional equations: the fractional Sawada&ndash;Kotera (SK) equation, the fractional Caudrey&ndash;Dodd&ndash;Gibbon (CDG) equation, and the fractional Kaup&ndash;Kuperschmidt (KK) equation. These equations represent special cases of the broader fractional fifth-order KdV equation. The novelty of this study lies in the application of LRPSM, which addresses the limitations of traditional methods by combining analytical precision with computational efficiency. The method successfully captures fractional dynamics, including soliton-like behaviors and memory effects, demonstrating its capability to model wave attenuation and smoothness influenced by fractional orders. The numerical results demonstrate that this method achieves minimal error margins, validating its robustness and precision in solving nonlinear fractional systems. Numerical examples validate the efficiency and robustness of this method, achieving high accuracy in solving nonlinear fractional systems. The results establish LRPSM as a versatile and reliable tool for solving fractional differential equations, paving the way for advancements in modern wave theory and applications across disciplines such as plasma physics, fluid mechanics, and nonlinear optics.OPEN ACCESS Received: 12/10/2024 Accepted: 21/01/2025 Published: 14/07/202

Rapid Assessment Tool for Haemophilus influenzae type b Disease in Developing Countries1

Haemophilus influenzae type b disease prevalence in children provides estimates of national disease prevalence

Global research priorities for interpersonal violence prevention: A modified Delphi study

© 2017, World Health Organization. All rights reserved. Objective To establish global research priorities for interpersonal violence prevention using a systematic approach. Methods Research priorities were identified in a three-round process involving two surveys. In round 1, 95 global experts in violence prevention proposed research questions to be ranked in round 2. Questions were collated and organized according to the four-step public health approach to violence prevention. In round 2, 280 international experts ranked the importance of research in the four steps, and the various substeps, of the public health approach. In round 3, 131 international experts ranked the importance of detailed research questions on the public health step awarded the highest priority in round 2. Findings In round 2, “developing, implementing and evaluating interventions” was the step of the public health approach awarded the highest priority for four of the six types of violence considered (i.e. child maltreatment, intimate partner violence, armed violence and sexual violence) but not for youth violence or elder abuse. In contrast, “scaling up interventions and evaluating their cost-effectiveness” was ranked lowest for all types of violence. In round 3, research into “developing, implementing and evaluating interventions” that addressed parenting or laws to regulate the use of firearms was awarded the highest priority. The key limitations of the study were response and attrition rates among survey respondents. However, these rates were in line with similar priority-setting exercises. Conclusion These findings suggest it is premature to scale up violence prevention interventions. Developing and evaluating smaller-scale interventions should be the funding priority

Ventilator-associated pneumonia in children after cardiac surgery in The Netherlands

We conducted a retrospective cohort study in an academic tertiary care center to characterize ventilator-associated pneumonia (VAP) in pediatric patients after cardiac surgery in The Netherlands. All patients following cardiac surgery and mechanically ventilated for ≥24 h were included. The primary outcome was development of VAP. Secondary outcomes were duration of mechanical ventilation and length of ICU stay. A total of 125 patients were enrolled. Their mean age was 16.5 months. The rate of VAP was 17.1/1,000 mechanical ventilation days. Frequently found organisms were Haemophilus influenzae, Moraxella catarrhalis, Staphylococcus aureus and Pseudomonas aeruginosa. Patients with VAP had longer duration of ventilation and longer ICU stay. Risk factors associated with the development of VAP were a PRISM III score of ≥10 and transfusion of fresh frozen plasma. The mean VAP rate in this population is higher than that reported in general pediatric ICU populations. Children with VAP had a prolonged need for mechanical ventilation and a longer ICU sta