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.  

SPATIOTEMPORAL TRANSMISSION DYNAMICS OF RECENT EBOLA OUTBREAK IN SIERRA LEONE, WEST AFRICA: IMPACT OF CONTROL MEASURES

2017 ◽  
Vol 25 (03) ◽  
pp. 369-397 ◽  
Author(s):  
PARIMITA ROY ◽  
RANJIT KUMAR UPADHYAY
Keyword(s):  
West Africa ◽  
Sierra Leone ◽  
Epidemic Model ◽  
Control Measure ◽  
Reaction Diffusion ◽  
Model System ◽  
Control Measures ◽  
Transmission Dynamics ◽  
Spatial Spread ◽  
The Impact

In this paper, we have formulated a compartmental epidemic model with exponentially decaying transmission rates to understand the Ebola transmission dynamics and study the impact of control measures to basic public health. The epidemic model exhibits two equilibria, namely, the disease-free and unique endemic equilibria. We have calculated the basic reproduction number through next generation matrix and investigated the spatial spread of the epidemic via reaction–diffusion modeling. Instead of fitting the model to the observed pattern of spread, we have used previously estimated parameter values and examined the efficacy of predictions of the designed model vis-à-vis the pattern of spread observed in Sierra Leone, West Africa. Further, we conducted a sensitivity analysis to determine the extent to which improvement in predictions is achievable through better parameterization.We performed numerical simulations with and without control measure for the designed model system. A significant reduction in infection and death cases were observed when proper control measures are incorporated in the model system. Two-dimensional simulation experiments show that infectious population and the number of deaths will increase up to one and a half years without control, but it will decline after two years. We have reported the numerical results, and it closely matches with the real situation in Sierra Leone.

scholarly journals Numerical techniques for stochastic foot and mouth disease epidemic model with the impact of vaccination

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Kamaleldin Abodayeh ◽  
Muhammad Shoaib Arif ◽  
Ali Raza ◽  
Muhammad Rafiq ◽  
Mairaj Bibi ◽  
...  
Keyword(s):  
Epidemic Model ◽  
Foot And Mouth Disease ◽  
Mouth Disease ◽  
Numerical Techniques ◽  
Foot And Mouth ◽  
The Impact

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 996. The Potential for Reducing Opioid and Analgesic Prescriptions Via Herpes Zoster Vaccination

2020 ◽  
Vol 7 (Supplement_1) ◽  
pp. S527-S527
Author(s):  
Jean-Etienne Poirrier ◽  
Justin Carrico ◽  
Jessica K DeMartino ◽  
Katherine A Hicks ◽  
Jeffrey J Stoddard ◽  
...  
Keyword(s):  
Herpes Zoster ◽  
Age Group ◽  
Opioid Prescription ◽  
Varicella Zoster ◽  
Effectiveness Model ◽  
Prescription Rates ◽  
Medication Exposure ◽  
The Mean ◽  
The Impact ◽  
Analgesic Use

Abstract Background Herpes zoster (HZ), or shingles, is a common neurocutaneous disease caused by the reactivation of latent varicella zoster virus that often includes rash and neuropathic pain that may last for months. Opioids and other analgesics may be prescribed. Recombinant zoster vaccine (RZV) is preferentially recommended for the prevention of HZ in adults aged 50 years and older. This study aimed to assess the impact of RZV vaccination on opioid and other analgesic prescription-related outcomes. Methods Estimates of analgesic prescription rates (opioids, benzodiazepines, and other analgesics) among HZ cases were established using Truven claims data from 2012-2018 for adults aged 50 years and older. HZ case avoidance with RZV vaccination was calculated using a previously published cost-effectiveness model. This data was included in a calculator assessing the impact of RZV vaccination on analgesic prescription-related outcomes (compared to no vaccination). Results Between 24.4% and 28.0% of HZ cases in the observed claims had at least one opioid prescription, dependent on age group (4.5%-6.5% and 8.6%-19.6% for benzodiazepines and other analgesics, respectively). The mean number of opioid prescriptions per person in each age group with at least one opioid prescription was between 1.7 and 1.9 (1.7-2.3 and 1.7-2.0 prescriptions for benzodiazepines and other analgesics, respectively). Assuming a 1-million-person population and 65% RZV coverage, the calculator predicts RZV vaccination will prevent 75,002 cases of HZ and will prevent 19,311 people from being prescribed at least 1 HZ-related opioid, 4,502 people from being prescribed benzodiazepines, and 12,201 people from being prescribed other analgesics. Additionally, 34,520 HZ-related opioid prescriptions will be avoided (9,413 benzodiazepine prescriptions; 22,406 other analgesic prescriptions). Conclusion HZ is associated with high levels of opioid, benzodiazepine, and other analgesic use. Primary prevention of HZ by vaccination could potentially reduce opioid and other medication exposure. Disclosures Jean-Etienne Poirrier, PhD, MBA, The GSK group of companies (Employee, Shareholder) Justin Carrico, BS, GlaxoSmithKline (Consultant) Jessica K. DeMartino, PhD, The GlaxoSmithKline group of companies (Employee, Shareholder) Katherine A. Hicks, MS, BSPH, GlaxoSmithKline (Scientific Research Study Investigator, GSK pays my company for my contractual services.) Saurabh P. Nagar, MS, RTI Health Solutions (Employee) Juliana Meyers, MA, GlaxoSmithKline (Other Financial or Material Support, This study was funded by GlaxoSmithKline.)

scholarly journals Modelling the impact of detection on COVID-19 transmission dynamics in Ghana

2021 ◽  
Vol 8 (1) ◽  
pp. 1953722
Author(s):  
Josiah Mushanyu ◽  
Zviiteyi Chazuka ◽  
Frenick Mudzingwa ◽  
Chisara Ogbogbo
Keyword(s):  
Transmission Dynamics ◽  
The Impact

scholarly journals The mathematics of multiple lockdowns

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Antonio Scala
Keyword(s):  
Beneficial Effect ◽  
Epidemic Model ◽  
Final Size ◽  
Optimal Response ◽  
Support Strategy ◽  
The Impact ◽  
New Strategies

AbstractWhile vaccination is the optimal response to an epidemic, recent events have obliged us to explore new strategies for containing worldwide epidemics, like lockdown strategies, where the contacts among the population are strongly reduced in order to slow down the propagation of the infection. By analyzing a classical epidemic model, we explore the impact of lockdown strategies on the evolution of an epidemic. We show that repeated lockdowns have a beneficial effect, reducing the final size of the infection, and that they represent a possible support strategy to vaccination policies.

scholarly journals Elucidating the Local Transmission Dynamics of Highly Pathogenic Avian Influenza H5N6 in the Republic of Korea by Integrating Phylogenetic Information

Pathogens ◽  
2021 ◽  
Vol 10 (6) ◽  
pp. 691
Author(s):  
Dae-Sung Yoo ◽  
Byungchul Chun ◽  
Kyung-Duk Min ◽  
Jun-Sik Lim ◽  
Oun-Kyoung Moon ◽  
...  
Keyword(s):  
Avian Influenza ◽  
Highly Pathogenic Avian Influenza ◽  
Transmission Dynamics ◽  
Republic Of Korea ◽  
Transmission Risk ◽  
Highly Pathogenic ◽  
Pathogenic Avian Influenza ◽  
The Republic ◽  
The Impact ◽  
Local Transmission

Highly pathogenic avian influenza (HPAI) virus is one of the most virulent and infectious pathogens of poultry. As a response to HPAI epidemics, veterinary authorities implement preemptive depopulation as a controlling strategy. However, mass culling within a uniform radius of the infection site can result in unnecessary depopulation. Therefore, it is useful to quantify the transmission distance from infected premises (IPs) before determining the optimal area for preemptive depopulation. Accordingly, we analyzed the transmission risk within spatiotemporal clusters of IPs using transmission kernel estimates derived from phylogenetic clustering information on 311 HPAI H5N6 IPs identified during the 2016–2017 epidemic, Republic of Korea. Subsequently, we explored the impact of varying the culling radius on the local transmission of HPAI given the transmission risk estimates. The domestic duck farm density was positively associated with higher transmissibility. Ring culling over a radius of 3 km may be effective for areas with high dense duck holdings, but this approach does not appear to significantly reduce the risk for local transmission in areas with chicken farms. This study provides the first estimation of the local transmission dynamics of HPAI in the Republic of Korea as well as insight into determining an effective ring culling radius.

scholarly journals A fractional order mathematical model for COVID-19 dynamics with quarantine, isolation, and environmental viral load

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mohammed A. Aba Oud ◽  
Aatif Ali ◽  
Hussam Alrabaiah ◽  
Saif Ullah ◽  
Muhammad Altaf Khan ◽  
...  
Keyword(s):  
Epidemic Model ◽  
Reproduction Number ◽  
Model Parameters ◽  
Disease Dynamics ◽  
Threshold Parameter ◽  
Fractional Model ◽  
Infected People ◽  
Fractional Models ◽  
Disease Epidemics ◽  
The Impact

AbstractCOVID-19 or coronavirus is a newly emerged infectious disease that started in Wuhan, China, in December 2019 and spread worldwide very quickly. Although the recovery rate is greater than the death rate, the COVID-19 infection is becoming very harmful for the human community and causing financial loses to their economy. No proper vaccine for this infection has been introduced in the market in order to treat the infected people. Various approaches have been implemented recently to study the dynamics of this novel infection. Mathematical models are one of the effective tools in this regard to understand the transmission patterns of COVID-19. In the present paper, we formulate a fractional epidemic model in the Caputo sense with the consideration of quarantine, isolation, and environmental impacts to examine the dynamics of the COVID-19 outbreak. The fractional models are quite useful for understanding better the disease epidemics as well as capture the memory and nonlocality effects. First, we construct the model in ordinary differential equations and further consider the Caputo operator to formulate its fractional derivative. We present some of the necessary mathematical analysis for the fractional model. Furthermore, the model is fitted to the reported cases in Pakistan, one of the epicenters of COVID-19 in Asia. The estimated value of the important threshold parameter of the model, known as the basic reproduction number, is evaluated theoretically and numerically. Based on the real fitted parameters, we obtained $\mathcal{R}_{0} \approx 1.50$ R 0 ≈ 1.50 . Finally, an efficient numerical scheme of Adams–Moulton type is used in order to simulate the fractional model. The impact of some of the key model parameters on the disease dynamics and its elimination are shown graphically for various values of noninteger order of the Caputo derivative. We conclude that the use of fractional epidemic model provides a better understanding and biologically more insights about the disease dynamics.

MODELING THE IMPACT OF VOLUNTARY TESTING AND TREATMENT ON TUBERCULOSIS TRANSMISSION DYNAMICS

2012 ◽  
Vol 05 (04) ◽  
pp. 1250029 ◽  
Author(s):  
S. MUSHAYABASA ◽  
C. P. BHUNU
Keyword(s):  
Deterministic Model ◽  
Reproduction Number ◽  
Positive Impact ◽  
Transmission Dynamics ◽  
Effective Control ◽  
Reproductive Number ◽  
Voluntary Testing ◽  
Manifold Theory ◽  
The Impact ◽  
Disease Free

A deterministic model for evaluating the impact of voluntary testing and treatment on the transmission dynamics of tuberculosis is formulated and analyzed. The epidemiological threshold, known as the reproduction number is derived and qualitatively used to investigate the existence and stability of the associated equilibrium of the model system. The disease-free equilibrium is shown to be locally-asymptotically stable when the reproductive number is less than unity, and unstable if this threshold parameter exceeds unity. It is shown, using the Centre Manifold theory, that the model undergoes the phenomenon of backward bifurcation where the stable disease-free equilibrium co-exists with a stable endemic equilibrium when the associated reproduction number is less than unity. The analysis of the reproduction number suggests that voluntary tuberculosis testing and treatment may lead to effective control of tuberculosis. Furthermore, numerical simulations support the fact that an increase voluntary tuberculosis testing and treatment have a positive impact in controlling the spread of tuberculosis in the community.

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