scholarly journals The effect of heterogeneous infectious period and contagiousness on the dynamics ofSalmonellatransmission in dairy cattle

2008 ◽  
Vol 136 (11) ◽  
pp. 1496-1510 ◽  
Author(s):  
C. LANZAS ◽  
S. BRIEN ◽  
R. IVANEK ◽  
Y. LO ◽  
P. P. CHAPAGAIN ◽  
...  
Keyword(s):  
Dairy Cattle ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Dynamics ◽  
Infectious Period ◽  
Specific Group ◽  
Infection Transmission ◽  
Force Of Infection ◽  
The Impact

SUMMARYThe objective of this study was to address the impact of heterogeneity of infectious period and contagiousness onSalmonellatransmission dynamics in dairy cattle populations. We developed three deterministic SIR-type models with two basic infected stages (clinically and subclinically infected). In addition, model 2 included long-term shedders, which were defined as individuals with low contagiousness but long infectious period, and model 3 included super-shedders (individuals with high contagiousness and long infectious period). The simulated dynamics, basic reproduction number (R0) and critical vaccination threshold were studied. Clinically infected individuals were the main force of infection transmission for models 1 and 2. Long-term shedders had a small impact on the transmission of the infection and on the estimated vaccination thresholds. The presence of super-shedders increasesR0and decreases the effectiveness of population-wise strategies to reduce infection, making necessary the application of strategies that target this specific group.

scholarly journals The impact of the undetected COVID-19 cases on its transmission dynamics

2020 ◽  
Author(s):  
Sujata Saha ◽  
Sumanta Saha
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Disease Risk ◽  
Transmission Dynamics ◽  
Transmission Model ◽  
Risk Of Infection ◽  
Infection Transmission ◽  
Reported Data ◽  
The Impact

AbstractObjectiveThe COVID-19 pandemic is currently ongoing. Presently, due to the unavailability of a definitive vaccine to decrease its acquiring, it’s essential to understand its transmissibility in the community by undetected cases to control its transmission. This study aims to study this context using mathematical modelling.MethodsA COVID-19 transmission model was framed that estimated the basic reproduction number (R0, a measurement of disease risk) using the next-generation method. It explored the contribution of exposed and infected (detected and undetected) individuals, and environmental pathogen to the overall risk of infection spreading, utilizing the publicly reported data of this infection in Maharashtra between March 22, 2020, and May 4, 2020. A sensitivity analysis was performed to study the effect of a rising number of undetected cases to R0.ResultsThe estimated basic reproduction number is R0 = 4.63, which increases rapidly with the rise in the undetected COVID-19 cases. Although the exposed individuals made the largest contribution to infection transmission (R1 = 2.42), the contaminated environment also played a significant role.ConclusionsIt is crucial to identify the individuals exposed and infected to COVID-19 disease and isolate them to control its transmission. The awareness of the role of fomites in infection transmission is also important in this regard.

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 Analysis of the Model on the Effect of Seasonal Factors on Malaria Transmission Dynamics

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Victor Yiga ◽  
Hasifa Nampala ◽  
Julius Tumwiine
Keyword(s):  
Malaria Transmission ◽  
Basic Reproduction Number ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Current Control ◽  
Transmission Dynamics ◽  
Mosquito Vector ◽  
The Impact ◽  
The Basic Reproduction Number

Malaria is one of the world’s most prevalent epidemics. Current control and eradication efforts are being frustrated by rapid changes in climatic factors such as temperature and rainfall. This study is aimed at assessing the impact of temperature and rainfall abundance on the intensity of malaria transmission. A human host-mosquito vector deterministic model which incorporates temperature and rainfall dependent parameters is formulated. The model is analysed for steady states and their stability. The basic reproduction number is obtained using the next-generation method. It was established that the mosquito population depends on a threshold value θ , defined as the number of mosquitoes produced by a female Anopheles mosquito throughout its lifetime, which is governed by temperature and rainfall. The conditions for the stability of the equilibrium points are investigated, and it is shown that there exists a unique endemic equilibrium which is locally and globally asymptotically stable whenever the basic reproduction number exceeds unity. Numerical simulations show that both temperature and rainfall affect the transmission dynamics of malaria; however, temperature has more influence.

scholarly journals Modeling Impact of Temperature and Human Movement on the Persistence of Dengue Disease

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Ganga Ram Phaijoo ◽  
Dil Bahadur Gurung
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Human Movement ◽  
Transmission Dynamics ◽  
Temperature Dependent ◽  
Dengue Disease ◽  
Movement Rates ◽  
Vector Borne ◽  
Temperature Levels ◽  
The Impact

Dengue is a vector-borne infectious disease endemic in many parts of the world. The disease is spreading in new places due to human movement into the dengue disease supporting areas. Temperature is the major climatic factor which affects the biological processes of the mosquitoes and their interaction with the viruses. In the present work, we propose a multipatch model to assess the impact of temperature and human movement in the transmission dynamics of dengue disease. The work consists of system of ordinary differential equations that describe the transmission dynamics of dengue disease between humans and mosquitoes. Human population is divided into four classes: susceptible, exposed, infectious, and recovered. Mosquito population is divided into three classes: susceptible, exposed, and infectious. Basic reproduction numberR0of the model is obtained using Next-Generation Matrix method. The qualitative analysis of the model is made in terms of the basic reproduction number. Parameters used in the model are considered temperature dependent. Dynamics of vector and host populations are investigated with different human movement rates and different temperature levels. Numerical results show that proper management of human movement between patches helps reducing the burden of dengue disease. It is also seen that the temperature affects the transmission dynamics of the disease significantly.

scholarly journals Impact of Hygiene on Malaria Transmission Dynamics: A Mathematical Model

2021 ◽  
Author(s):  
Temidayo Oluwafemi ◽  
Emmanuel Azuaba
Keyword(s):  
Mathematical Model ◽  
Malaria Transmission ◽  
Basic Reproduction Number ◽  
Human Population ◽  
Reproduction Number ◽  
Model System ◽  
Transmission Dynamics ◽  
The Impact ◽  
Disease Free ◽  
The Basic Reproduction Number

Malaria continues to pose a major public health challenge, especially in developing countries, 219 million cases of malaria were estimated in 89 countries. In this paper, a mathematical model using non-linear differential equations is formulated to describe the impact of hygiene on Malaria transmission dynamics, the model is analyzed. The model is divided into seven compartments which includes five human compartments namely; Unhygienic susceptible human population, Hygienic Susceptible Human population, Unhygienic infected human population , hygienic infected human population and the Recovered Human population  and the mosquito population is subdivided into susceptible mosquitoes  and infected mosquitoes . The positivity of the solution shows that there exists a domain where the model is biologically meaningful and mathematically well-posed. The Disease-Free Equilibrium (DFE) point of the model is obtained, we compute the Basic Reproduction Number using the next generation method and established the condition for Local stability of the disease-free equilibrium, and we thereafter obtained the global stability of the disease-free equilibrium by constructing the Lyapunov function of the model system. Also, sensitivity analysis of the model system was carried out to identify the influence of the parameters on the Basic Reproduction Number, the result shows that the natural death rate of the mosquitoes is most sensitive to the basic reproduction number.

scholarly journals Analysis and Modeling of Tuberculosis Transmission Dynamics

2019 ◽  
pp. 1-14
Author(s):  
Rodah Jerubet ◽  
George Kimathi ◽  
Mary Wanaina
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Transmission Dynamics ◽  
Sensitive Parameter ◽  
Latently Infected ◽  
Model Equations ◽  
The Impact ◽  
Disease Free ◽  
The Basic Reproduction Number

Mycobacterium tuberculosis is the causative agent of Tuberculosis in humans [1,2]. A mathematical model that explains the transmission of Tuberculosis is developed. The model consists of four compartments; the susceptible humans, the infectious humans, the latently infected humans, and the recovered humans. We conducted an analysis of the disease-free equilibrium and endemic equilibrium points. We also computed the basic reproduction number using the next generation matrix approach. The disease-free equilibrium was found to be asymptotically stable if the reproduction number was less than one. The most sensitive parameter to the basic reproduction number was also determined using sensitivity analysis. Recruitment and contact rate are the most sensitive parameter that contributes to the basic reproduction number. Ordinary Differential Equations is used in the for­mulation of the model equations. The Tuberculosis model is analyzed in order to give a proper account of the impact of its transmission dynamics and the effect of the latent stage in TB transmission. The steady state's solution of the model is investigated. The findings showed that as more people come into contact with infectious individuals, the spread of TB would increase. The latent rate of infection below a critical value makes TB infection to persist.   However, the recovery rate of infectious individuals is an indication that the spread of the disease will reduce with time which could help curb TB transmission. 

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 Modelling the Evolution of COVID-19 in High-Incidence European Countries and Regions: Estimated Number of Infections and Impact of Past and Future Intervention Measures

2020 ◽  
Vol 9 (6) ◽  
pp. 1825 ◽  
Author(s):  
Juan Fernández-Recio
Keyword(s):  
Reproduction Number ◽  
Mechanistic Model ◽  
Control Measures ◽  
European Countries ◽  
Intervention Measures ◽  
High Incidence ◽  
Future Outcomes ◽  
Long Term Impact ◽  
The Impact

A previously developed mechanistic model of COVID-19 transmission has been adapted and applied here to study the evolution of the disease and the effect of intervention measures in some European countries and territories where the disease has had a major impact. A clear impact of the major intervention measures on the reproduction number (Rt) has been found in all studied countries and territories, as already suggested by the drop in the number of deaths over time. Interestingly, the impact of such major intervention measures seems to be the same in most of these countries. The model has also provided realistic estimates of the total number of infections, active cases and future outcomes. While the predictive capabilities of the model are much more uncertain before the peak of the outbreak, we could still reliably predict the evolution of the disease after a major intervention by assuming the subsequent reproduction number from the current study. A greater challenge is to foresee the long-term impact of softer intervention measures, but this model can estimate the outcome of different scenarios and help to plan changes for the implementation of control measures in a given country or region.

A THEORETICAL ASSESSMENT OF THE EFFECTS OF DISTRIBUTED DELAY ON THE TRANSMISSION DYNAMICS OF HEPATITIS B

2015 ◽  
Vol 23 (03) ◽  
pp. 423-455
Author(s):  
P. MOUOFO TCHINDA ◽  
JEAN JULES TEWA ◽  
BOULECHARD MEWOLI ◽  
SAMUEL BOWONG
Keyword(s):  
Drug Therapy ◽  
Hepatitis B ◽  
Basic Reproduction Number ◽  
Disease Transmission ◽  
Time Delays ◽  
Reproduction Number ◽  
Distributed Delay ◽  
Global Dynamics ◽  
The Impact ◽  
The Basic Reproduction Number

In this paper, we investigate the global dynamics of a system of delay differential equations which describes the interaction of hepatitis B virus (HBV) with both liver and blood cells. The model has two distributed time delays describing the time needed for infection of cell and virus replication. We also include the efficiency of drug therapy in inhibiting viral production and the efficiency of drug therapy in blocking new infection. We compute the basic reproduction number and find that increasing delays will decrease the value of the basic reproduction number. We study the sensitivity analysis on the key parameters that drive the disease dynamics in order to determine their relative importance to disease transmission and prevalence. Our analysis reveals that the model exhibits the phenomenon of backward bifurcation (where a stable disease-free equilibrium (DFE) co-exists with a stable endemic equilibrium when the basic reproduction number is less than unity). Numerical simulations are presented to evaluate the impact of time-delays on the prevalence of the disease.

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