scholarly journals An Efficient Numerical Method for the Solution of the Polio Virus (Poliomyelitis) Epidemic Model with the Role of Vaccination

2020 ◽  
Vol 4 (4) ◽  
pp. 15-30
Author(s):  
Muhammad Rafique ◽  
Naveed Shahid ◽  
Nauman Ahmed ◽  
Tahira Sumbal Shaikh ◽  
Muhammad Asif ◽  
...  
Keyword(s):  
Epidemic Model ◽  
Numerical Scheme ◽  
Numerical Solutions ◽  
Communicable Disease ◽  
Continuous System ◽  
Transmission Dynamics ◽  
Polio Virus ◽  
Standard Methods ◽  
Nsfd Scheme

Mathematical modeling of a communicable disease is an effective way to describe the behavior and dynamics of the disease. It builds on our understanding of the transmission of a contagion in a population. In this paper, we explore the transmission dynamics of the polio virus (poliomyelitis) with vaccination using standard methods. We formulate an unconditionally stable Non-Standard Finite Difference (NSFD) scheme for a continuous system of the epidemic polio virus. The designed scheme to approximate the solution is bounded, consistent with the underlying model. The proposed numerical scheme preserves the positivity of the stated variables which is necessary for any population dynamical system. It is used to calculate the numerical solutions of the epidemic model for different step sizes “h”. Two other numerical schemes are enforced to find the solution of the proposed system. Finally, the comparison of the NSFD technique with these methods proves its validity and effectiveness.

scholarly journals An unconditionally positive and global stability preserving NSFD scheme for an epidemic model with vaccination

2014 ◽  
Vol 24 (3) ◽  
pp. 635-646 ◽  
Author(s):  
Deqiong Ding ◽  
Qiang Ma ◽  
Xiaohua Ding
Keyword(s):  
Numerical Simulation ◽  
Global Stability ◽  
Difference Equations ◽  
Epidemic Model ◽  
Lyapunov Functions ◽  
Numerical Solutions ◽  
Time Step ◽  
The Stability ◽  
Nsfd Scheme ◽  
Nonstandard Finite Difference

Abstract In this paper, a NonStandard Finite Difference (NSFD) scheme is constructed, which can be used to determine numerical solutions for an epidemic model with vaccination. Here the NSFD method is employed to derive a set of difference equations for the epidemic model with vaccination. We show that difference equations have the same dynamics as the original differential system, such as the positivity of the solutions and the stability of the equilibria, without being restricted by the time step. Our proof of global stability utilizes the method of Lyapunov functions. Numerical simulation illustrates the effectiveness of our results

scholarly journals A Reliable Numerical Analysis of Transmission Dynamics of Chicken Pox (Varicella Zoster Virus)

2020 ◽  
Vol 4 (4) ◽  
pp. 31-45
Author(s):  
Muhammad Rafiq ◽  
Nauman Ahmed ◽  
Mudassar Rafique ◽  
Muhammad Ozair Ahmad
Keyword(s):  
Epidemic Model ◽  
Numerical Approximation ◽  
Numerical Technique ◽  
Transmission Dynamics ◽  
Numerical Techniques ◽  
Varicella Zoster ◽  
Physical Traits ◽  
The Impact ◽  
Nsfd Scheme ◽  
Real World Problems

Solutions generated through numerical techniques are great in solving real-world problems. This manuscript deals with the numerical approximation of the epidemic system, describing the transmission dynamics of the Vercilla Zoster Virus (VZV) through the impact of vaccination. To discretize the continuous dynamical system, we proposed a novel numerical technique that preserves the true dynamics of the VZV epidemic model. The proposed technique is established in such a manner that it sustains all necessary physical traits depicted by the epidemic model under study. The designed technique is named a nonstandard finite difference (NSFD) scheme. Theoretical analysis of the designed NSFD technique is presented which describes its strength over the standard numerical procedures which are already being used for such purposes. The graphical solutions of all the numerical techniques are presented which verify the efficacy of the proposed NSFDS technique.  

scholarly journals Integrating additional knowledge into the estimation of graphical models

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Yunqi Bu ◽  
Johannes Lederer
Keyword(s):  
Graphical Models ◽  
Tuning Parameter ◽  
Functional Magnetic Resonance ◽  
Resonance Imaging ◽  
Graphical Modeling ◽  
Standard Methods ◽  
Neighborhood Selection ◽  
Selection For ◽  
The Brain

Abstract Graphical models such as brain connectomes derived from functional magnetic resonance imaging (fMRI) data are considered a prime gateway to understanding network-type processes. We show, however, that standard methods for graphical modeling can fail to provide accurate graph recovery even with optimal tuning and large sample sizes. We attempt to solve this problem by leveraging information that is often readily available in practice but neglected, such as the spatial positions of the measurements. This information is incorporated into the tuning parameter of neighborhood selection, for example, in the form of pairwise distances. Our approach is computationally convenient and efficient, carries a clear Bayesian interpretation, and improves standard methods in terms of statistical stability. Applied to data about Alzheimer’s disease, our approach allows us to highlight the central role of lobes in the connectivity structure of the brain and to identify an increased connectivity within the cerebellum for Alzheimer’s patients compared to other subjects.

scholarly journals The role of infant nutrition in the global epidemic of non-communicable disease

2016 ◽  
Vol 75 (2) ◽  
pp. 162-168 ◽  
Author(s):  
Atul Singhal
Keyword(s):  
Early Life ◽  
Infant Nutrition ◽  
Communicable Disease ◽  
Bottle Feeding ◽  
Postnatal Life ◽  
World Region ◽  
Global Epidemic ◽  
Main Determinants ◽  
The Impact

Non-communicable diseases (NCD) and atherosclerotic CVD in particular, are the most important health problems of the 21st century. Already in every world region except Africa, NCD account for greater mortality than communicable, maternal, perinatal and nutritional conditions combined. Although modifiable lifestyle factors in adults are the main determinants, substantial evidence now suggests that factors in early life also have a major role in the development of NCD; commonly referred to as the Developmental Origins of Health and Disease hypothesis. Factors in utero, early postnatal life and throughout childhood, have been shown to affect NCD by influencing risk factors for CVD such as obesity, diabetes, hypertension and dyslipidaemia. Infant nutrition (e.g. breastfeeding rather than bottle feeding) and a slower pattern of infant weight gain have been shown to be particularly protective against later risk of obesity and CVD in both low- and high-income countries. The mechanisms involved are poorly understood, but include epigenetic changes; effects on endocrine systems regulating body weight, food intake and fat deposition; and changes in appetite regulation. As a consequence, strategies to optimise early life nutrition could make a major contribution to stemming the current global epidemic of NCD. This review will consider the role of early life factors in the development of NCD, focusing on the impact of infant nutrition/growth on obesity and CVD. The review will highlight the experimental (randomised) evidence where available, briefly summarise the underlying mechanisms involved and consider the implications for public health.

ROLE OF REINFECTION IN TRANSMISSION DYNAMICS OF COVID-19: A SEMI-ANALYTICAL APPROACH USING DIFFERENTIAL TRANSFORM METHOD

2021 ◽  
Vol 6 (1) ◽  
pp. 745
Author(s):  
Opeyemi Odetunde ◽  
Jibril Lawal ◽  
Ally Yeketi Ayinla
Keyword(s):  
Treatment Strategies ◽  
Differential Transform Method ◽  
Host Community ◽  
Transmission Dynamics ◽  
Transform Method ◽  
Social Distancing ◽  
Linear System Of Equations ◽  
Differential Transform ◽  
Non Linear System

Reinfection of a recovered individual either as a result of relapse or new contact no doubt poses a major threat to the eradication of an infection within the host community. In this work, the role of re-infection in the transmission dynamics of COVID-19 was considered and analysed using the semi-analytical tool Differential Transform Method (DTM). COVID-19 (also known as Coronavirus) has shut down the economy of the world since it became a global pandemic. A mathematical model was constructed with consideration of multiple pathways of infection transmission, the treatment strategies and policies adopted (social distancing, wearing of face mask and so on) to limit the spread of the infection globally. The non-linear system of equations governing the model was solved using DTM and the resulting series solution was compared with the standard numeric Runge-Kutta order 4 (RK4). It was discovered that re-integration of a recovered individual into the susceptible community without observing the prevention guidelines such as social distancing, washing of hands and proper sanitizing could increase the spread of the infection since the recovered individuals are not guaranteed of immunity against the infection after recovery. The study concluded that families of recovered patients must ensure adequate preventive measure while integrating their recovered loved ones back to their midst.

scholarly journals SIR Model for Dengue Disease with Effect of Dengue Vaccination

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Pratchaya Chanprasopchai ◽  
I. Ming Tang ◽  
Puntani Pongsumpun
Keyword(s):  
Mathematical Model ◽  
Mortality Rate ◽  
Dengue Virus ◽  
Numerical Solutions ◽  
Specific Treatment ◽  
Sir Model ◽  
Dengue Vaccine ◽  
Dengue Disease ◽  
Modelling Methods

The dengue disease is caused by dengue virus, and there is no specific treatment. The medical care by experienced physicians and nurses will save life and will lower the mortality rate. A dengue vaccine to control the disease is available in Thailand since late 2016. A mathematical model would be an important way to analyze the effects of the vaccination on the transmission of the disease. We have formulated an SIR (susceptible-infected-recovered) model of the transmission of the disease which includes the effect of vaccination and used standard dynamical modelling methods to analyze the effects. The equilibrium states and their stabilities are investigated. The trajectories of the numerical solutions plotted into the 2D planes and 3D spaces are presented. The main contribution is determining the role of dengue vaccination in the model. From the analysis, we find that there is a significant reduction in the total hospitalization time needed to treat the illness.

scholarly journals Precision Medicine, Developmental Plasticity and Prevention of Non-Communicable Disease

2020 ◽  
Author(s):  
Carol Wang ◽  
John Attia ◽  
Stephen Lye ◽  
Wendy Oddy ◽  
Lawrence Beilin ◽  
...  
Keyword(s):  
Precision Medicine ◽  
Early Life ◽  
Developmental Plasticity ◽  
Communicable Disease ◽  
Adult Health ◽  
Lower Systolic Blood Pressure ◽  
Adult Disease ◽  
Healthy Nutrition ◽  
Non Communicable Disease

Abstract Background: It is well established that genetics, environment, and interplay between them play crucial roles in adult disease. We aimed to evaluate the role of genetics, early life nutrition, and interaction between them, on optimal adult health. Methods: As part of a large international consortium (n~154,000), we identified 60 SNPs associated with both birthweight and adult disease. Utilising the Raine Study, we developed a birthweight polygenic score (BW-PGS) based the 60 SNPs and examined relationships between BW-PGS and adulthood cardiovascular risk factors, specifically evaluating interactions with early life nutrition. Findings: Healthy nutrition was beneficial for all individuals; longer duration of any breastfeeding was associated with lower BMI and lower Systolic Blood Pressure in those with higher BW-PGS. Interpretation: Optimal breastfeeding offers the greatest benefit to reduce adult obesity and hypertension in those genetically predisposed to high birthweight. This provides an example of how precision medicine in early life can improve adult health.

scholarly journals On the relative role of different age groups during influenza A epidemics in Germany, 2002-2017

2017 ◽  
Author(s):  
Edward Goldstein
Keyword(s):  
Influenza A ◽  
Communicable Disease ◽  
Age Groups ◽  
School Age Children ◽  
Relative Role ◽  
School Age ◽  
Limited Information ◽  
School Students ◽  
Using Data

AbstractBackgroundThere is limited information about the role of different age groups, particularly subgroups of school-age children and younger adults in propagating influenza epidemics.MethodsFor a communicable disease outbreak, some subpopulations may play a disproportionate role during the ascent of the outbreak due to increased susceptibility and/or contact rates. Such subpopulations can be identified by considering the proportion that cases in a subpopulation represent among all cases in the population occurring before the epidemic peak (Bp), the corresponding proportion after the epidemic peak (Ap), to calculate the relative risk for a subpopulation, RR=Bp/Ap. We estimated RR for several age groups using data on reported influenza A cases in Germany between 2002-2017.ResultsChildren aged 14-17y had the highest RR estimates for 7 out of 15 influenza A epidemics in the data, including the 2009 pandemic, and the large 2016/17, 2008/09, and 2006/07 seasons. Children aged 10-13y had the highest RR estimates during 3 epidemics, including the large 2014/15 and 2004/05 seasons. Children aged 6-9y had the highest RR estimates during two epidemics, including the large 2012/13 season. Children aged 2-5y had the highest RR estimate during the moderate 2015/16 season; adults aged 18-24y had the highest RR estimate during the small 2005/06 season; adults aged 25-34y had the highest RR estimate during the large, 2002/03 season.ConclusionsOur results support the prominent role of all school-age children, particularly the oldest ones, in propagating influenza epidemics in the community. We note that national vaccination coverage levels among older school-age children were lower than among younger school-age children during the recent influenza seasons in the US, and influenza vaccination program in England has not been phased in yet for secondary school students.

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