Two Dynamic Models About Rabies Between Dogs and Human

Wang, Xiaowei; Lou, Jie

doi:10.1142/s0218339008002666

Cited by 17 publications

(14 citation statements)

References 7 publications

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“…An ordinary differential equation model was used to characterize the transmission dynamics of rabies between humans and dogs by [21,22]. The work by Zinsstag et al [23] further extended the existing models on rabies transmission between dogs to include dogto-human transmission and concluded that human postexposure prophylaxis (PEP) with a dog vaccination campaign was the more cost effective in controlling the disease in the long run.…”

Section: Introductionmentioning

confidence: 99%

Modelling of Rabies Transmission Dynamics Using Optimal Control Analysis

Asamoah

Oduro

Bonyah

et al. 2017

Journal of Applied Mathematics

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We examine an optimal way of eradicating rabies transmission from dogs into the human population, using preexposure prophylaxis (vaccination) and postexposure prophylaxis (treatment) due to public education. We obtain the disease-free equilibrium, the endemic equilibrium, the stability, and the sensitivity analysis of the optimal control model. Using the Latin hypercube sampling (LHS), the forward-backward sweep scheme and the fourth-order Range-Kutta numerical method predict that the global alliance for rabies control's aim of working to eliminate deaths from canine rabies by 2030 is attainable through mass vaccination of susceptible dogs and continuous use of pre-and postexposure prophylaxis in humans.

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Section: Introductionmentioning

confidence: 99%

Modelling of Rabies Transmission Dynamics Using Optimal Control Analysis

Asamoah

Oduro

Bonyah

et al. 2017

Journal of Applied Mathematics

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“…Carroll et al [11] created a continuous compartmental model to describe rabies epidemiology in dog populations and explored three control methods: vaccination, vaccination plus fertility control, and culling. Wang and Lou [96] and Yang and Lou [109] used ordinary differential equation models to characterize the transmission dynamics of rabies between humans and dogs. Zinsstag et al [117] extended existing models on rabies transmission between dogs to include dog-to-human transmission and concluded that combining human PEP with a dog-vaccination campaign is more cost-effective in the long run.…”

Section: Introductionmentioning

confidence: 99%

Modeling the transmission dynamics and control of rabies in China

Ruan

2017

Mathematical Biosciences

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Human rabies was first recorded in ancient China in about 556 BC and is still one of the major public-health problems in China. From 1950 to 2015, 130,494 human rabies cases were reported in Mainland China with an average of 1977 cases per year. It is estimated that 95% of these human rabies cases are due to dog bites. The purpose of this article is to provide a review about the models, results, and simulations that we have obtained recently on studying the transmission of rabies in China. We first construct a basic susceptible, exposed, infectious, and recovered (SEIR) type model for the spread of rabies virus among dogs and from dogs to humans and use the model to simulate the human rabies data in China from 1996 to 2010. Then we modify the basic model by including both domestic and stray dogs and apply the model to simulate the human rabies data from Guangdong Province, China. To study the seasonality of rabies, in Section 4 we further propose a SEIR model with periodic transmission rates and employ the model to simulate the monthly data of human rabies cases reported by the Chinese Ministry of Health from January 2004 to December 2010. To understand the spatial spread of rabies, in Section 5 we add diffusion to the dog population in the basic SEIR model to obtain a reaction-diffusion equation model and determine the minimum wave speed connecting the disease-free equilibrium to the endemic equilibrium. Finally, in order to investigate how the movement of dogs affects the geographically inter-provincial spread of rabies in Mainland China, in Section 6 we propose a multi-patch model to describe the transmission dynamics of rabies between dogs and humans and use the two-patch submodel to investigate the rabies virus clades lineages and to simulate the human rabies data from Guizhou and Guangxi, Hebei and Fujian, and Sichuan and Shaanxi, respectively. Some discussions are provided in Section 7.

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“…The choice of which control strategy is most effective depending on the disease and its epidemiological characteristics. For most directly transmissible diseases, culling or vaccination alone has been shown to be more appropriate, whereas for others, a combination of both methods is the most optimal strategy . For our model, culling is related with mortality rate, birth rate, density‐dependent reduction in birth rate, loss of resistance, and the transmission coefficient whereas vaccination will directly influence the recovery rate and the transmission rate.…”

Section: Numerical Simulationsmentioning

confidence: 99%

Mathematical analysis of the transmission dynamics of brucellosis among bison

Abatih

Ron

Speybroeck

et al. 2014

Math Methods in App Sciences

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In this study, a mathematical model previously proposed for the transmission dynamics of brucellosis among bison was mathematically analyzed. Our qualitative and quantitative findings support the general hypothesis that the infection will vanish from the herd when the basic reproduction number R0<1 and will persist otherwise. A global sensitivity analysis was conducted, and the results of the Sobol indices indicated that the rate of loss of resistance (δ) and the recovery rate (v) were responsible for most of the variability in the expected number of infectious bison. On the other hand, according to the partial ranked correlation coefficients, the density‐dependent reduction in birth (φ), the mortality rate (m), the transmission coefficient (β), and the recovery rate (v) exerted very high (and negative) correlations with the number of infectious bison, whereas the rate of loss of resistance (δ) and the calving rate (a) exerted very high (and positive) correlations with the number of infectious bison. Control measures should therefore aim at increasing the magnitude of φ, m, and v and reducing those of δ and a. In addition, experimental studies are needed to precisely estimate the rate of loss of resistance and the recovery rate in order to increase the accuracy of the expected number of infectious bison. Copyright © 2014 John Wiley & Sons, Ltd.

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Two Dynamic Models About Rabies Between Dogs and Human

Cited by 17 publications

References 7 publications

Modelling of Rabies Transmission Dynamics Using Optimal Control Analysis

Modelling of Rabies Transmission Dynamics Using Optimal Control Analysis

Modeling the transmission dynamics and control of rabies in China

Mathematical analysis of the transmission dynamics of brucellosis among bison

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