Ruan2017 - Transmission dynamics and control of rabies in China

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  • Modeling the transmission dynamics and control of rabies in China.
  • Ruan S
  • Mathematical biosciences , 4/ 2017 , Volume 286 , pages: 65-93 , PubMed ID: 28188732
  • Department of Mathematics, University of Miami, Coral Gables, FL 33146, USA. Electronic address:
  • 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.
Submitter of the first revision: Sarubini Kananathan
Submitter of this revision: Sarubini Kananathan
Modellers: Sarubini Kananathan

Metadata information

is (2 statements)
BioModels Database MODEL1808280012
BioModels Database BIOMD0000000726

isDescribedBy (1 statement)
PubMed 28188732

hasTaxon (3 statements)
hasProperty (2 statements)
Mathematical Modelling Ontology Ordinary differential equation model
NCIt Rabies

Curation status


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Model files

Model.xml SBML L2V4 representation of Ruan2017 - Transmission dynamics and control of rabies in China 64.46 KB Preview | Download

Additional files

Modelling the transmission dynamics and control of rabies in china REACTIONS.cps Copasi file for the model. Figure produced is similar to publication. 90.32 KB Preview | Download

  • Model originally submitted by : Sarubini Kananathan
  • Submitted: Aug 28, 2018 4:38:27 PM
  • Last Modified: Dec 6, 2018 10:35:02 AM
  • Version: 6 public model Download this version
    • Submitted on: Dec 6, 2018 10:35:02 AM
    • Submitted by: Sarubini Kananathan
    • With comment: Automatically added model identifier BIOMD0000000726
  • Version: 4 public model Download this version
    • Submitted on: Aug 28, 2018 4:38:27 PM
    • Submitted by: Sarubini Kananathan
    • With comment: Edited model metadata online.

(*) You might be seeing discontinuous revisions as only public revisions are displayed here. Any private revisions unpublished model revision of this model will only be shown to the submitter and their collaborators.

: Variable used inside SBML models

Species Initial Concentration/Amount
S h

0000514 ; Homo sapiens
1.29E9 mol
E h

exposure ; Homo sapiens
250.0 mol
I h

0000511 ; Homo sapiens
89.0 mol
R h

Recovered or Resolved ; Homo sapiens
200000.0 mol
E d

exposure ; Canis lupus familiaris
200000.0 mol
S d

0000514 ; Canis lupus familiaris
3.5E7 mol
Reactions Rate Parameters
S_h => Human_Population*m_h*S_h m_h = 0.003
E_h => Human_Population*m_h*E_h m_h = 0.003
E_h => R_h Human_Population*k_h*E_h k_h = 0.54
I_h => Human_Population*m_h*I_h m_h = 0.003
R_h => S_h Human_Population*lambda_h*R_h lambda_h = 1.0
E_d => I_d compartment*sigma*gamma*E_d gamma = 0.4; sigma = 6.0
S_h => E_h; I_d beta_dh*S_h*I_d beta_dh = 2.29E-12
R_h => Human_Population*m_h*R_h m_h = 0.003
S_d => E_d; I_d compartment*beta*S_d*I_d beta = 1.58E-7
Curator's comment:
(added: 06 Dec 2018, 10:33:32, updated: 06 Dec 2018, 10:33:32)
Figure 2.2b of the reference publication has been reproduced. Initial conditions were taken from the publication. The parameter values of mu_h and m_h had to be changed to 1.34 and 0.003 respectively to reproduce a figure similar to the publication. The model was simulated using Copasi 4.24 and the figure was generated using Python 3.7.