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 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.

scholarly journals Analysis and Prediction of COVID-19 Characteristics Using a Birth-and-Death Model

2020 ◽  
Author(s):  
Narayanan C. Viswanath
Keyword(s):  
Mathematical Modeling ◽  
Infectious Diseases ◽  
Explicit Expression ◽  
Basic Reproduction Number ◽  
Stationary Point ◽  
Reproduction Number ◽  
Sir Model ◽  
Expected Number ◽  
Infection Period ◽  
The Basic Reproduction Number

AbstractIts spreading speed together with the risk of fatality might be the main characteristic that separates COVID-19 from other infectious diseases in our recent history. In this scenario, mathematical modeling for predicting the spread of the disease could have great value in containing the disease. Several very recent papers have contributed to this purpose. In this study we propose a birth-and-death model for predicting the number of COVID-19 active cases. It relation to the Susceptible-Infected-Recovered (SIR) model has been discussed. An explicit expression for the expected number of active cases helps us to identify a stationary point on the infection curve, where the infection ceases increasing. Parameters of the model are estimated by fitting the expressions for active and total reported cases simultaneously. We analyzed the movement of the stationary point and the basic reproduction number during the infection period up to the 20th of April 2020. These provide information about the disease progression path and therefore could be really useful in designing containment strategies.

scholarly journals Uncertainty and sensitivity analysis of the basic reproduction number of diphtheria: a case study of a Rohingya refugee camp in Bangladesh, November–December 2017

PeerJ ◽  
2018 ◽  
Vol 6 ◽  
pp. e4583 ◽  
Author(s):  
Ryota Matsuyama ◽  
Andrei R. Akhmetzhanov ◽  
Akira Endo ◽  
Hyojung Lee ◽  
Takayuki Yamaguchi ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Basic Reproduction Number ◽  
Process Model ◽  
Large Scale ◽  
Reproduction Number ◽  
Latin Hypercube Sampling ◽  
Refugee Camp ◽  
Background Information ◽  
The Basic Reproduction Number

BackgroundA Rohingya refugee camp in Cox’s Bazar, Bangladesh experienced a large-scale diphtheria epidemic in 2017. The background information of previously immune fraction among refugees cannot be explicitly estimated, and thus we conducted an uncertainty analysis of the basic reproduction number,R0.MethodsA renewal process model was devised to estimate theR0and ascertainment rate of cases, and loss of susceptible individuals was modeled as one minus the sum of initially immune fraction and the fraction naturally infected during the epidemic. To account for the uncertainty of initially immune fraction, we employed a Latin Hypercube sampling (LHS) method.ResultsR0ranged from 4.7 to 14.8 with the median estimate at 7.2.R0was positively correlated with ascertainment rates. Sensitivity analysis indicated thatR0would become smaller with greater variance of the generation time.DiscussionEstimatedR0was broadly consistent with published estimate from endemic data, indicating that the vaccination coverage of 86% has to be satisfied to prevent the epidemic by means of mass vaccination. LHS was particularly useful in the setting of a refugee camp in which the background health status is poorly quantified.

scholarly journals Mathematical Assessment of the Dynamical Model of Smoking Tobacco Epidemic in Bangladesh

2020 ◽  
pp. 36-48
Author(s):  
Sk. Abdus Samad ◽  
Md. Tusberul Islam ◽  
Sayed Toufiq Hossain Tomal ◽  
MHA Biswas
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Stability Analysis ◽  
Differential Equations ◽  
Basic Reproduction Number ◽  
Conversion Rate ◽  
Reproduction Number ◽  
The World ◽  
Tobacco Epidemic ◽  
The Basic Reproduction Number

Bangladesh is one of the largest tobacco users in the world being troubled by smoking related issues. In this paper we consider a compartmental mathematical model of smoking in which the population is divided into five compartments: susceptible, expose, smokers, temporary quitters and permanent quitters described by ordinary differential equations. We study by including the conversion rate from light smoker to permanent quit smokers. The basic reproduction number R0 has been derived and then we found two euilibria of the model one of them is smoking-free and other of them is smoking-present. We establish the positivity, boundedness of the solutions and perform stability analysis of the model. To decrease the smoking propensity in Bangladesh we perform numerical simulation for various estimations of parameters which offer understanding to give up smoking and how they influence the smoker and exposed class. This model gives us legitimate thought regarding the explanations for the spread of smoking in Bangladesh.

scholarly journals A Susceptible Exposed Infected Recovered Susceptible (SEIRS) Model for the Transmission of Tuberculosis

2021 ◽  
Vol 47 (3) ◽  
pp. 917-927
Author(s):  
Latifat M. Erinle-Ibrahim ◽  
Waheed O Lawal ◽  
Olukayode Adebimpe ◽  
Gbemisola R Sontan
Keyword(s):  
Numerical Simulation ◽  
Sensitivity Analysis ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Tb Treatment ◽  
Latent Tb ◽  
Keywords Epidemiology ◽  
Age Structured ◽  
Susceptible Populations ◽  
Age Structured Model

In this paper, a deterministic mathematical model was proposed and analyzed to understand the dynamics of tuberculosis based on the SEIRS model. The disease-free equilibrium, the endemic equilibrium, and their stabilities were examined. The R0 (basic reproduction number) was derived using the Next Generation Matrix method and its sensitivity analysis showed that the birth rate and infectious rate were the most sensitive parameters of R0. The behaviour of exposed individuals at the latent period with varied treatment rates were examined through numerical simulation. From the analysis carried out, the effect of variations of the treatments of latent TB shows that it affects the disease burden. This implies that testing and treatment of latent TB are important in preventing it from becoming infectious. The re-infection rate was examined to see the effect it had both on the recovered and susceptible populations. The study concludes by recommending the extension of the model to an age structured model with co-infection with another respiratory infectious disease like COVID-19. Keywords: Epidemiology; Latent TB treatment; Basic Reproduction Number; sensitivity analysis; numerical simulation

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