scholarly journals Seasonal Treatment of an Infectious Disease is a Social Driver of Sustained Oscillations in the Disease incidence

2021 ◽  
Vol 22 (2) ◽  
pp. 279-289
Author(s):  
O. Osuna ◽  
J. G. Villavicencio Pulido
Keyword(s):  
Infectious Disease ◽  
Periodic Solutions ◽  
Disease Incidence ◽  
Degree Theory ◽  
Sir Model ◽  
Treatment Rate ◽  
Sustained Oscillations ◽  
Periodic Treatment

We analyze a seasonal $SIR$ model that assumes a periodic treatment rate. Using the Leray-Schauder degree theory, we prove that model shows periodic solutions. This result shows that sustained oscillations in the incidence of the disease are related to the periodic application of a treatment against the disease. So, we can say that the periodic application of treatment can be considered a seasonal driver of the sustained oscillations.

scholarly journals Permanence and Positive Periodic Solutions of a Discrete Delay Competitive System

2010 ◽  
Vol 2010 ◽  
pp. 1-22 ◽  
Author(s):  
Wenjie Qin ◽  
Zhijun Liu
Keyword(s):  
Periodic Solutions ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Discrete Delay ◽  
Positive Periodic Solutions ◽  
Competitive System ◽  
Discrete Function ◽  
Species Population

A discrete time non-autonomous two-species competitive system with delays is proposed, which involves the influence of many generations on the density of species population. Sufficient conditions for permanence of the system are given. When the system is periodic, by using the continuous theorem of coincidence degree theory and constructing a suitable Lyapunov discrete function, sufficient conditions which guarantee the existence and global attractivity of positive periodic solutions are obtained. As an application, examples and their numerical simulations are presented to illustrate the feasibility of our main results.

scholarly journals Improving Hand Hygiene Compliance in Nursing Homes: Protocol for a Cluster Randomized Controlled Trial (HANDSOME Study)

10.2196/17419 ◽  
2020 ◽  
Vol 9 (5) ◽  
pp. e17419 ◽  
Author(s):  
Gwen R Teesing ◽  
Vicki Erasmus ◽  
Mariska Petrignani ◽  
Marion P G Koopmans ◽  
Miranda de Graaf ◽  
...  
Keyword(s):  
Infectious Disease ◽  
Nursing Homes ◽  
Hand Hygiene ◽  
Hand Hygiene Compliance ◽  
Disease Incidence ◽  
Controlled Trial ◽  
World Health ◽  
The World ◽  
Hygiene Compliance ◽  
Cluster Randomized

Background Hand hygiene compliance is considered the most (cost-)effective measure for preventing health care–associated infections. While hand hygiene interventions have frequently been implemented and assessed in hospitals, there is limited knowledge about hand hygiene compliance in other health care settings and which interventions and implementation methods are effective. Objective This study aims to evaluate the effect of a multimodal intervention to increase hand hygiene compliance of nurses in nursing homes through a cluster randomized controlled trial (HANDSOME study). Methods Nursing homes were randomly allocated to 1 of 3 trial arms: receiving the intervention at a predetermined date, receiving the identical intervention after an infectious disease outbreak, or serving as a control arm. Hand hygiene was evaluated in nursing homes by direct observation at 4 timepoints. We documented compliance with the World Health Organization’s 5 moments of hand hygiene, specifically before touching a patient, before a clean/aseptic procedure, after body fluid exposure risk, after touching a patient, and after touching patient surroundings. The primary outcome is hand hygiene compliance of the nurses to the standards of the World Health Organization. The secondary outcome is infectious disease incidence among residents. Infectious disease incidence was documented by a staff member at each nursing home unit. Outcomes will be compared with the presence of norovirus, rhinovirus, and Escherichia coli on surfaces in the nursing homes, as measured using quantitative polymerase chain reaction. Results The study was funded in September 2015. Data collection started in October 2016 and was completed in October 2017. Data analysis will be completed in 2020. Conclusions HANDSOME studies the effectiveness of a hand hygiene intervention specifically for the nursing home environment. Nurses were taught the World Health Organization’s 5 moments of hand hygiene guidelines using the slogan “Room In, Room Out, Before Clean, After Dirty,” which was developed for nursing staff to better understand and remember the hygiene guidelines. HANDSOME should contribute to improved hand hygiene practice and a reduction in infectious disease rates and related mortality. Trial Registration Netherlands Trial Register (NTR6188) NL6049; https://www.trialregister.nl/trial/6049 International Registered Report Identifier (IRRID) DERR1-10.2196/17419

scholarly journals Stability and Hopf-Bifurcation Analysis of Delayed BAM Neural Network under Dynamic Thresholds

2009 ◽  
Vol 14 (4) ◽  
pp. 435-461 ◽  
Author(s):  
P. D. Gupta ◽  
N. C. Majee ◽  
A. B. Roy
Keyword(s):  
Hopf Bifurcation ◽  
Periodic Solutions ◽  
Global Bifurcation ◽  
Distributed Delay ◽  
Degree Theory ◽  
Homotopy Invariance ◽  
Normal Form Theory ◽  
Form Theory ◽  
Bam Neural Network ◽  
Uniqueness Of Equilibrium

In this paper the dynamics of a three neuron model with self-connection and distributed delay under dynamical threshold is investigated. With the help of topological degree theory and Homotopy invariance principle existence and uniqueness of equilibrium point are established. The conditions for which the Hopf-bifurcation occurs at the equilibrium are obtained for the weak kernel of the distributed delay. The direction and stability of the bifurcating periodic solutions are determined by the normal form theory and central manifold theorem. Lastly global bifurcation aspect of such periodic solutions is studied. Some numerical simulations for justifying the theoretical analysis are also presented.

scholarly journals The attainment of herd immunity with a reducing risk of contact infection in modelling 

2021 ◽  
Author(s):  
Kian Boon Law ◽  
Kalaiarasu M Peariasamy ◽  
Hishamshah Ibrahim ◽  
Noor Hisham Abdullah
Keyword(s):  
Infectious Disease ◽  
Disease Transmission ◽  
Herd Immunity ◽  
Sir Model ◽  
Mixed Population ◽  
Transmission Model ◽  
Force Of Infection ◽  
Initial Stage ◽  
And Control ◽  
Model Features

Abstract The risk of contact infection among susceptible individuals in a randomly mixed population can be reduced by the presence of immune individuals and this principle forms the fundamental of herd immunity. The conventional susceptible-infectious-recovered (SIR) model features an infection-induced herd immunity model, but does not include the reducing risk of contact infection among susceptible individuals in the transmission model, therefore tends to overestimate the transmission dynamics of infectious diseases. Here we show that the reducing risk of contact infection among susceptible individuals can be achieved by incorporating the proportion of susceptible individuals (model A) or the inverse of proportion of recovered individuals (model B) in the force of infection of the SIR model. We numerically simulated the conventional SIR model and both new SIR models A and B under the exact condition with a basic reproduction number of 3·0. Prior to the numerical simulation, the threshold for the eradication of infectious disease through herd immunity was expected to be 0·667 (66·7%) for all three models. All three models performed likewise at the initial stage of disease transmission. In the conventional SIR model, the infectious disease subsided when 94·0 % of the population had been infected and recovered, way above the expected threshold for eradication and control of the infectious disease. Both models A and B simulated the infectious disease to diminish when 66·7% and 75·6% of the population had been infected, showing herd immunity might protect more susceptible individuals from the infectious disease as compared to the projection generated by the conventional SIR. Our study shows that model A provides a better framework for modelling herd immunity through vaccination, while model B provides a better framework for modelling herd immunity through infection. Both models overcome the insufficiency of the conventional SIR model in attaining the effect of herd immunity in modelling outputs, which is important and relevant for modelling infectious disease, such as the COVID-19 in a randomly mixed population.

On the time periodic thermistor problem

2004 ◽  
Vol 15 (1) ◽  
pp. 55-77 ◽  
Author(s):  
WALTER ALLEGRETTO ◽  
YANPING LIN ◽  
SHUQING MA
Keyword(s):  
Periodic Solutions ◽  
Degree Theory ◽  
Time Behaviour ◽  
Uniform Attractor ◽  
Long Time Behaviour ◽  
Galerkin Approximations ◽  
Long Time ◽  
Finite Dimensionality ◽  
Time Periodic Solutions ◽  
Time Periodic

In this paper we study a nonlocal parabolic/elliptic system which models thermistor behaviour in cases where heat losses to the surrounding gas play a significant role. The existence of time periodic solutions for the system is established through Faedo-Galerkin approximations and the Leray–Schauder degree theory. We show that for the small gas pressure case, the temperature of the time periodic solutions is positive. Moreover we consider the long time behaviour of the system and prove the existence of a uniform attractor. Finally, the finite dimensionality of the attractor is discussed.

scholarly journals Translating surveillance data into incidence estimates

2019 ◽  
Vol 374 (1776) ◽  
pp. 20180262 ◽  
Author(s):  
Y. Bourhis ◽  
T. Gottwald ◽  
F. van den Bosch
Keyword(s):  
Infectious Disease ◽  
Disease Incidence ◽  
Disease Outbreaks ◽  
Estimation Methods ◽  
Estimation Model ◽  
Theme Issue ◽  
Online Application ◽  
Infectious Disease Outbreaks ◽  
Sampling Series ◽  
Wide Range

Monitoring a population for a disease requires the hosts to be sampled and tested for the pathogen. This results in sampling series from which we may estimate the disease incidence, i.e. the proportion of hosts infected. Existing estimation methods assume that disease incidence does not change between monitoring rounds, resulting in an underestimation of the disease incidence. In this paper, we develop an incidence estimation model accounting for epidemic growth with monitoring rounds that sample varying incidence. We also show how to accommodate the asymptomatic period that is the characteristic of most diseases. For practical use, we produce an approximation of the model, which is subsequently shown to be accurate for relevant epidemic and sampling parameters. Both the approximation and the full model are applied to stochastic spatial simulations of epidemics. The results prove their consistency for a very wide range of situations. The estimation model is made available as an online application. This article is part of the theme issue ‘Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control’. This theme issue is linked with the earlier issue ‘Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes’.

scholarly journals Positive Periodic Solutions of Cooperative Systems with Delays and Feedback Controls

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Tursuneli Niyaz ◽  
Ahmadjan Muhammadhaji
Keyword(s):  
Periodic Solutions ◽  
Continuous Time ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Continuation Theorem ◽  
Positive Periodic Solutions ◽  
Feedback Controls ◽  
Volterra Systems

This paper studies a class of periodicnspecies cooperative Lotka-Volterra systems with continuous time delays and feedback controls. Based on the continuation theorem of the coincidence degree theory developed by Gaines and Mawhin, some new sufficient conditions on the existence of positive periodic solutions are established.

scholarly journals Global Attractivity of a Periodic DelayedN-Species Model of Facultative Mutualism

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Ahmadjan Muhammadhaji ◽  
Zhidong Teng
Keyword(s):  
Lyapunov Function ◽  
Periodic Solutions ◽  
Function Method ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Positive Periodic Solutions ◽  
Facultative Mutualism ◽  
Lyapunov Function Method

Two classes of periodicN-species Lotka-Volterra facultative mutualism systems with distributed delays are discussed. Based on the continuation theorem of the coincidence degree theory developed by Gaines and Mawhin and the Lyapunov function method, some new sufficient conditions on the existence and global attractivity of positive periodic solutions are established.

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