scholarly journals The Impact of Awareness Programs with Recruitment and Delay on the Spread of an Epidemic

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Lixia Zuo ◽  
Maoxing Liu ◽  
Jinqiang Wang
Keyword(s):  
Reproduction Number ◽  
Recruitment Rate ◽  
Limited Extent ◽  
Implementation Rate ◽  
Awareness Programs ◽  
And Control ◽  
The Impact ◽  
The Relationship ◽  
Disease Free ◽  
Two Equilibria

A compartment epidemic model with delay is given to discuss the impact of awareness programs on the spread and control of infectious diseases in a given region. It is assumed that there is a constant recruitment rate in the cumulative density of awareness programs, and further it is assumed that awareness programs can influence the susceptible to a limited extent. The system exhibits two equilibria: the disease-free equilibrium is stable if the basic reproduction number is less than unity for any delay and the unique endemic equilibrium exhibits Hopf-bifurcation under certain conditions. Numerical simulations prove the results of analysis and the significance of awareness programs in preventing and controlling the diseases, by investigating the relationship between the proportion of the infective and the dissemination rate and the implementation rate, respectively.

scholarly journals A Mathematical Model of Treatment and Vaccination Interventions of Pneumococcal Pneumonia Infection Dynamics

2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Mohammed Kizito ◽  
Julius Tumwiine
Keyword(s):  
Reproduction Number ◽  
Control Strategies ◽  
The Elderly ◽  
Infection Dynamics ◽  
And Control ◽  
Long Term Behavior ◽  
The Impact ◽  
Globally Stable ◽  
Disease Free

Streptococcus pneumoniae is one of the leading causes of serious morbidity and mortality worldwide, especially in young children and the elderly. In this study, a model of the spread and control of bacterial pneumonia under public health interventions that involve treatment and vaccination is formulated. It is found out that the model exhibits the disease-free and endemic equilibria. The disease-free equilibrium is stable if and only if the basic reproduction number R0<1 and the disease will be wiped out of the population. For R0≥1, the endemic equilibrium is globally stable and the disease persists. We infer the effect of these interventions on the dynamics of the pneumonia through sensitivity analysis on the effective reproduction number Re, from which it is revealed that treatment and vaccination interventions combined can eradicate pneumonia infection. Numerical simulation to illustrate the analytical results and establish the long term behavior of the disease is done. The impact of pneumonia infection control strategies is investigated. It is revealed that, with treatment and vaccination interventions combined, pneumonia can be wiped out. However, with treatment intervention alone, pneumonia persists in the population.

scholarly journals Threshold Dynamics in a Model for Zika Virus Disease with Seasonality

2021 ◽  
Vol 83 (4) ◽  
Author(s):  
Mahmoud A. Ibrahim ◽  
Attila Dénes
Keyword(s):  
Zika Virus ◽  
Reproduction Number ◽  
Virus Disease ◽  
Threshold Dynamics ◽  
Global Dynamics ◽  
Threshold Parameter ◽  
Globally Asymptotically Stable ◽  
Linear Integral ◽  
The Impact ◽  
Disease Free

AbstractWe present a compartmental population model for the spread of Zika virus disease including sexual and vectorial transmission as well as asymptomatic carriers. We apply a non-autonomous model with time-dependent mosquito birth, death and biting rates to integrate the impact of the periodicity of weather on the spread of Zika. We define the basic reproduction number $${\mathscr {R}}_{0}$$ R 0 as the spectral radius of a linear integral operator and show that the global dynamics is determined by this threshold parameter: If $${\mathscr {R}}_0 < 1,$$ R 0 < 1 , then the disease-free periodic solution is globally asymptotically stable, while if $${\mathscr {R}}_0 > 1,$$ R 0 > 1 , then the disease persists. We show numerical examples to study what kind of parameter changes might lead to a periodic recurrence of Zika.

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.

scholarly journals Threshold Dynamics of a Huanglongbing Model with Logistic Growth in Periodic Environments

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Jianping Wang ◽  
Shujing Gao ◽  
Yueli Luo ◽  
Dehui Xie
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Logistic Growth ◽  
Threshold Dynamics ◽  
Global Dynamics ◽  
Globally Asymptotically Stable ◽  
Linear Integral ◽  
The Impact ◽  
Disease Free ◽  
The Basic Reproduction Number

We analyze the impact of seasonal activity of psyllid on the dynamics of Huanglongbing (HLB) infection. A new model about HLB transmission with Logistic growth in psyllid insect vectors and periodic coefficients has been investigated. It is shown that the global dynamics are determined by the basic reproduction numberR0which is defined through the spectral radius of a linear integral operator. IfR0< 1, then the disease-free periodic solution is globally asymptotically stable and ifR0> 1, then the disease persists. Numerical values of parameters of the model are evaluated taken from the literatures. Furthermore, numerical simulations support our analytical conclusions and the sensitive analysis on the basic reproduction number to the changes of average and amplitude values of the recruitment function of citrus are shown. Finally, some useful comments on controlling the transmission of HLB are given.

scholarly journals The Impact of the Direct Participation of Workers on the Rates of Absenteeism in the Spanish Labor Environment

2020 ◽  
Vol 17 (7) ◽  
pp. 2477 ◽  
Author(s):  
Raúl Payá Castiblanque
Keyword(s):  
Multinomial Logistic Regression ◽  
Management Plan ◽  
Risk Prevention ◽  
Prevention Measures ◽  
Direct Participation ◽  
High Level ◽  
And Control ◽  
The Impact ◽  
The Relationship ◽  
Transversal Study

The aim of this research was to study the relationship between the different levels of direct participation of workers (passive, consultative or active-delegated) in risk prevention management with the levels of absenteeism in Spain. To this end, a transversal study was carried out using microdata from the Second European Survey of Companies on New and Emerging Risks (ESENER-2-Spain, 2014) with a master population of 3162 work centres. A multinomial logistic regression model was carried out, with the dependent variable being the levels of absenteeism and the independent variables, the participation indicators and preventive management, calculating the adjusted odds ratio (aOR) between all the independent and control variables, with their corresponding 95% confidence intervals (95% IC). The results obtained showed how the active-delegative participation of workers in the design and adoption of psychosocial risk prevention measures reported 2.33 less probabilities of having a very high or fairly high level of absenteeism (aOR = 0.43; 95%IC:0.27–0.69). However, having documented aspects of preventive management (plan, risk assessment, planning measures) did not have any impact on absenteeism levels, which shows that we can fall into an unrealistic institutional mirage of security with active policies of co-education or co-management being necessary to reduce absenteeism.

scholarly journals The impact of air quality on its Baidu index: grey model analysis

2021 ◽  
Author(s):  
Leping Tu ◽  
Yan Chen
Keyword(s):  
Air Pollution ◽  
Air Quality ◽  
Quality Index ◽  
Air Quality Index ◽  
Grey Correlation ◽  
Convolution Model ◽  
Grey Correlation Analysis ◽  
And Control ◽  
The Impact ◽  
The Relationship

Abstract To investigate the relationship between air quality and its Baidu index, we collect the annual Baidu index of air pollution hazards, causes and responses. Grey correlation analysis, particle swarm optimization and grey multivariate convolution model are used to simulate and forecast the comprehensive air quality index. The result shows that the excessive growth of the comprehensive air quality index will lead to an increase in the corresponding Baidu index. The number of search for the causes of air quality has the closest link with the comprehensive air quality index. Strengthening the awareness of public about air pollution is conducive to the improvement of air quality. The result provides a reference for relevant departments to prevent and control air pollution.

5. Partners and Each Other

2020 ◽  
pp. 157-204
Author(s):  
Geoffrey Morse ◽  
Thomas Braithwaite
Keyword(s):  
Good Faith ◽  
Fiduciary Duties ◽  
Detailed Consideration ◽  
Internal Management ◽  
Contractual Agreements ◽  
And Control ◽  
The Impact ◽  
The Relationship

This chapter concerns the relationship between partners and the interface between the contractual and fiduciary duties implicit in such a relationship, including the internal management of the firm. It examines the impact of equity on contractual agreements, including the doctrine of forfeiture. The nebulous overriding duty of good faith is followed by the statutory duties of honesty, no conflict/no profit and no competition. The implied terms in relation to management (including access to partnership information) and control, financial affairs (detailing capital, capital profits and income profits) and the limits on change of partners are followed by a detailed consideration of the validity and exercise of expulsion clauses. Finally, the chapter details the limited effects of both voluntary and involuntary assignments of a partner's share.

scholarly journals Analysis of a malaria model with mosquito host choice and bed-net control

2015 ◽  
Vol 08 (06) ◽  
pp. 1550077 ◽  
Author(s):  
Bruno Buonomo
Keyword(s):  
Reproduction Number ◽  
Host Choice ◽  
Bed Nets ◽  
Bed Net ◽  
Host Manipulation ◽  
Host Preferences ◽  
Insecticide Treated Bed Nets ◽  
The Impact ◽  
Malaria Model ◽  
Disease Free

A malaria model is formulated which includes the enhanced attractiveness of infectious humans to mosquitoes, as result of host manipulation by malaria parasite, and the human behavior, represented by insecticide-treated bed-nets usage. The occurrence of a backward bifurcation at R0 = 1 is shown to be possible, which implies that multiple endemic equilibria co-exist with a stable disease-free equilibrium when the basic reproduction number is less than unity. This phenomenon is found to be caused by disease-induced human mortality. The global asymptotic stability of the endemic equilibrium for R0 > 1 is proved, by using the geometric method for global stability. Therefore, the disease becomes endemic for R0 > 1 regardless of the number of initial cases in both the human and vector populations. Finally, the impact on system dynamics of vector's host preferences and bed-net usage behavior is investigated.

scholarly journals Seasonality Impact on the Transmission Dynamics of Tuberculosis

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Yali Yang ◽  
Chenping Guo ◽  
Luju Liu ◽  
Tianhua Zhang ◽  
Weiping Liu
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Autonomous Systems ◽  
Positive Periodic Solution ◽  
Transmission Dynamics ◽  
Uniform Persistence ◽  
Globally Asymptotically Stable ◽  
The Impact ◽  
Disease Free ◽  
The Basic Reproduction Number

The statistical data of monthly pulmonary tuberculosis (TB) incidence cases from January 2004 to December 2012 show the seasonality fluctuations in Shaanxi of China. A seasonality TB epidemic model with periodic varying contact rate, reactivation rate, and disease-induced death rate is proposed to explore the impact of seasonality on the transmission dynamics of TB. Simulations show that the basic reproduction number of time-averaged autonomous systems may underestimate or overestimate infection risks in some cases, which may be up to the value of period. The basic reproduction number of the seasonality model is appropriately given, which determines the extinction and uniform persistence of TB disease. If it is less than one, then the disease-free equilibrium is globally asymptotically stable; if it is greater than one, the system at least has a positive periodic solution and the disease will persist. Moreover, numerical simulations demonstrate these theorem results.

scholarly journals A co-infection model for Two-Strain Malaria and Cholera with Optimal Control

2020 ◽  
Author(s):  
Kenneth Uzoma Egeonu ◽  
Simeon Chioma Inyama ◽  
Andrew Omame
Keyword(s):  
Optimal Control ◽  
Drug Resistance ◽  
Necessary Conditions ◽  
Reproduction Number ◽  
Dynamical Property ◽  
Backward Bifurcation ◽  
Infection Model ◽  
Existence Of Optimal Control ◽  
The Impact ◽  
Disease Free

A mathematical model for two strains of Malaria and Cholera with optimal control is studied and analyzed to assess the impact of treatment controls in reducing the burden of the diseases in a population, in the presence of malaria drug resistance. The model is shown to exhibit the dynamical property of backward bifurcation when the associated reproduction number is less than unity. The global asymptotic stability of the disease-free equilibrium of the model is proven not to exist. The necessary conditions for the existence of optimal control and the optimality system for the model is established using the Pontryagin's Maximum Principle. Numerical simulations of the optimal control model reveal that malaria drug resistance can greatly influence the co-infection cases averted, even in the presence of treatment controls for co-infected individuals.

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