scholarly journals A Dynamic Model of Human and Livestock Tuberculosis Spread and Control in Urumqi, Xinjiang, China

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Shan Liu ◽  
Aiqiao Li ◽  
Xiaomei Feng ◽  
Xueliang Zhang ◽  
Kai Wang
Keyword(s):  
Sensitivity Analysis ◽  
Confidence Interval ◽  
Dynamic Model ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Model Parameters ◽  
Epidemiological Investigation ◽  
Dynamical Behaviors ◽  
And Control ◽  
The Basic Reproduction Number

We establish a dynamical model for tuberculosis of humans and cows. For the model, we firstly give the basic reproduction numberR0. Furthermore, we discuss the dynamical behaviors of the model. By epidemiological investigation of tuberculosis among humans and livestock from 2007 to 2014 in Urumqi, Xinjiang, China, we estimate the parameters of the model and study the transmission trend of the disease in Urumqi, Xinjiang, China. The reproduction number in Urumqi for the model is estimated to be 0.1811 (95% confidence interval: 0.123–0.281). Finally, we perform some sensitivity analysis of several model parameters and give some useful comments on controlling the transmission of tuberculosis.

scholarly journals Mathematical analysis of a measles transmission dynamics model in Bangladesh with double dose vaccination

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Md Abdul Kuddus ◽  
M. Mohiuddin ◽  
Azizur Rahman
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Equilibrium Points ◽  
Rank Correlation ◽  
Dynamical Analysis ◽  
Model Parameters ◽  
Progression Rate ◽  
Double Dose ◽  
The Basic Reproduction Number

AbstractAlthough the availability of the measles vaccine, it is still epidemic in many countries globally, including Bangladesh. Eradication of measles needs to keep the basic reproduction number less than one $$(\mathrm{i}.\mathrm{e}. \, \, {\mathrm{R}}_{0}<1)$$ ( i . e . R 0 < 1 ) . This paper investigates a modified (SVEIR) measles compartmental model with double dose vaccination in Bangladesh to simulate the measles prevalence. We perform a dynamical analysis of the resulting system and find that the model contains two equilibrium points: a disease-free equilibrium and an endemic equilibrium. The disease will be died out if the basic reproduction number is less than one $$(\mathrm{i}.\mathrm{e}. \, \, {\mathrm{ R}}_{0}<1)$$ ( i . e . R 0 < 1 ) , and if greater than one $$(\mathrm{i}.\mathrm{e}. \, \, {\mathrm{R}}_{0}>1)$$ ( i . e . R 0 > 1 ) epidemic occurs. While using the Routh-Hurwitz criteria, the equilibria are found to be locally asymptotically stable under the former condition on $${\mathrm{R}}_{0}$$ R 0 . The partial rank correlation coefficients (PRCCs), a global sensitivity analysis method is used to compute $${\mathrm{R}}_{0}$$ R 0 and measles prevalence $$\left({\mathrm{I}}^{*}\right)$$ I ∗ with respect to the estimated and fitted model parameters. We found that the transmission rate $$(\upbeta )$$ ( β ) had the most significant influence on measles prevalence. Numerical simulations were carried out to commissions our analytical outcomes. These findings show that how progression rate, transmission rate and double dose vaccination rate affect the dynamics of measles prevalence. The information that we generate from this study may help government and public health professionals in making strategies to deal with the omissions of a measles outbreak and thus control and prevent an epidemic in Bangladesh.

scholarly journals Rich Dynamics of a Brucellosis Model with Transport

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Juan Liang ◽  
Zhirong Zhao ◽  
Can Li
Keyword(s):  
Numerical Simulation ◽  
Sensitivity Analysis ◽  
Infectious Diseases ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Great Influence ◽  
Stable State ◽  
Initial Values ◽  
Si Model ◽  
The Basic Reproduction Number

Brucellosis is one of the major infectious diseases in China. In this study, we consider an SI model of animal brucellosis with transport. The basic reproduction number ℛ0 is obtained, and the stable state of the equilibria is analyzed. Numerical simulation shows that different initial values have a great influence on results of the model. In addition, the sensitivity analysis of ℛ0 with respect to different parameters is analyzed. The results reveal that the transport has dual effects. Specifically, transport can lead to increase in the number of infected animals; besides, transport can also reduce the number of infected animals in a certain range. The analysis shows that the number of infected animals can be controlled if animals are transported reasonably.

scholarly journals Modeling Transmission Dynamics ofStreptococcus suiswith Stage Structure and Sensitivity Analysis

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Chaojian Shen ◽  
Mingtao Li ◽  
Wei Zhang ◽  
Ying Yi ◽  
Youming Wang ◽  
...  
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Stage Structure ◽  
Sensitivity Analyses ◽  
Effective Control ◽  
Model Parameters ◽  
Global Dynamics ◽  
Deterministic Dynamic ◽  
Globally Stable ◽  
The Basic Reproduction Number

Streptococcosis is one of the major infectious and contagious bacterial diseases for swine farm in southern China. The influence of various control measures on the outbreaks and transmission ofS. suisis not currently known. In this study, in order to explore effective control and prevention measures we studied a deterministic dynamic model with stage structure forS. suis. The basic reproduction numberℛ0is identified and global dynamics are completely determined byℛ0. It shows that ifℛ0<1, the disease-free equilibrium is globally stable and the disease dies out, whereas ifℛ0>1, there is a unique endemic equilibrium which is globally stable and thus the disease persists in the population. The model simulations well agree with new clinical cases and the basic reproduction number of this model is about 1.1333. Some sensitivity analyses ofℛ0in terms of the model parameters are given. Our study demonstrates that combination of vaccination and disinfection of the environment are the useful control strategy forS. suis.

scholarly journals Threshold parameters for a model of epidemic spread among households and workplaces

2009 ◽  
Vol 6 (40) ◽  
pp. 979-987 ◽  
Author(s):  
L. Pellis ◽  
N. M. Ferguson ◽  
C. Fraser
Keyword(s):  
Infectious Disease ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Model Parameters ◽  
Epidemic Spread ◽  
Threshold Parameter ◽  
Disease Epidemiology ◽  
Infectious Disease Epidemiology ◽  
Complex Models ◽  
The Basic Reproduction Number

The basic reproduction number R 0 is one of the most important concepts in modern infectious disease epidemiology. However, for more realistic and more complex models than those assuming homogeneous mixing in the population, other threshold quantities can be defined that are sometimes more useful and easily derived in terms of model parameters. In this paper, we present a model for the spread of a permanently immunizing infection in a population socially structured into households and workplaces/schools, and we propose and discuss a new household-to-household reproduction number R H for it. We show how R H overcomes some of the limitations of a previously proposed threshold parameter, and we highlight its relationship with the effort required to control an epidemic when interventions are targeted at randomly selected households.

scholarly journals Sustainable social distancing through facemask use and testing during the Covid-19 pandemic

2020 ◽  
Author(s):  
Diego Chowell ◽  
Kimberlyn Roosa ◽  
Ranu Dhillon ◽  
Gerardo Chowell ◽  
Devabhaktuni Srikrishna
Keyword(s):  
Basic Reproduction Number ◽  
Symptom Onset ◽  
Social Protection ◽  
Reproduction Number ◽  
Type Model ◽  
Protective Behaviors ◽  
Social Distancing ◽  
And Control ◽  
Different Levels ◽  
The Basic Reproduction Number

We investigate how individual protective behaviors, different levels of testing, and isolation influence the transmission and control of the COVID-19 pandemic. Based on an SEIR-type model incorporating asymptomatic but infectious individuals (40%), we show that the pandemic may be readily controllable through a combination of testing, treatment if necessary, and self-isolation after testing positive (TTI) of symptomatic individuals together with social protection (e.g., facemask use, handwashing). When the basic reproduction number, R0, is 2.4, 65% effective social protection alone (35% of the unprotected transmission) brings the R below 1. Alternatively, 20% effective social protection brings the reproduction number below 1.0 so long as 75% of the symptomatic population is covered by TTI within 12 hours of symptom onset. Even with 20% effective social protection, TTI of 1 in 4 symptomatic individuals can substantially 'flatten the curve' cutting the peak daily incidence in half.

scholarly journals Estimation of the basic reproduction number, average incubation time, asymptomatic infection rate, and case fatality rate for COVID-19: Meta-analysis and sensitivity analysis

2020 ◽  
Author(s):  
Wenqing He ◽  
Grace Y. Yi ◽  
Yayuan Zhu
Keyword(s):  
Confidence Interval ◽  
Basic Reproduction Number ◽  
Incubation Time ◽  
Case Fatality Rate ◽  
Reproduction Number ◽  
Meta Analysis ◽  
Case Fatality ◽  
Asymptomatic Infection ◽  
Fatality Rate ◽  
The Basic Reproduction Number

AbstractThe coronavirus disease 2019 (COVID-19) has been found to be caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). However, comprehensive knowledge of COVID-19 remains incomplete and many important features are still unknown. This manuscripts conduct a meta-analysis and a sensitivity study to answer the questions: What is the basic reproduction number? How long is the incubation time of the disease on average? What portion of infections are asymptomatic? And ultimately, what is the case fatality rate? Our studies estimate the basic reproduction number to be 3.15 with the 95% interval (2.41, 3.90), the average incubation time to be 5.08 days with the 95% confidence interval (4.77, 5.39) (in day), the asymptomatic infection rate to be 46% with the 95% confidence interval (18.48%, 73.60%), and the case fatality rate to be 2.72% with 95% confidence interval (1.29%, 4.16%) where asymptomatic infections are accounted for.

scholarly journals Mathematical Model Analysis and Simulation of Visceral Leishmaniasis, Kashgar, Xinjiang, 2004–2016

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-14 ◽  
Author(s):  
Yateng Song ◽  
Tailei Zhang ◽  
Hui Li ◽  
Kai Wang ◽  
Xiaobo Lu
Keyword(s):  
Sensitivity Analysis ◽  
Visceral Leishmaniasis ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Parasite Infection ◽  
Parasitic Disease ◽  
Kala Azar ◽  
Si Model ◽  
The Basic Reproduction Number ◽  
Kashgar Prefecture

Visceral leishmaniasis (VL), known as kala-azar, is a serious parasitic disease. After malaria, VL is the second largest parasitic killer. This paper focuses on the VL transmission around sandflies, dogs, and people. Kashgar is located on the southwestern edge of Xinjiang, where kala-azar parasite infection occurs every year. According to the cases reported in the Kashgar Prefecture from 2004 to 2016, we proposed a dynamic model based on these three populations. The SEIR model was established for human population, the SI model was established for sandfly population, and the SI model was established for dog population. We fitted the model to cumulative cases from 2004 to 2016 for the epidemic in Kashgar and predicted that the cumulative incidence of kala-azar in Kashgar would continue to increase, but its growth rate would gradually slow down, which means that the number of cases would gradually decrease every year. We also estimated the basic reproduction number R0 = 1.76 (95% CI: 1.49–1.93). The sensitivity analysis shows that the mutual infection between sandfly and dog contributes the most to the basic reproduction number, while the transmission proportion of sandfly to the susceptible person and the mutual infection between sandfly and dog contribute the most to the number of leishmaniasis human cases. Therefore, according to the sensitivity analysis results, reducing the contact between sandflies and dogs is an effective way to reduce kala-azar.

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