Journal article
Analysis of cholera epidemics with bacterial growth and spatial movement
Journal of biological dynamics, Vol.9(sup1), pp.233-261
06/30/2015
Handle:
https://hdl.handle.net/2376/105596
PMID: 25363286
Abstract
In this work, we propose novel epidemic models (named, susceptible-infected-recovered-susceptible-bacteria) for cholera dynamics by incorporating a general formulation of bacteria growth and spatial variation. In the first part, a generalized ordinary differential equation (ODE) model is presented and it is found that bacterial growth contributes to the increase in the basic reproduction number,
. With the derived basic reproduction number, we analyse the local and global dynamics of the model. Particularly, we give a rigorous proof on the endemic global stability by employing the geometric approach. In the second part, we extend the ODE model to a partial differential equation (PDE) model with the inclusion of diffusion to capture the movement of human hosts and bacteria in a heterogeneous environment. The disease threshold of this PDE model is studied again by using the basic reproduction number. The results on the threshold dynamics of the ODE and PDE models are compared, and verified through numerical simulation. Additionally, our analysis shows that incorporating diffusive spatial spread does not produce a Turing instability when
associated with the ODE model is less than the unity.
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Details
- Title
- Analysis of cholera epidemics with bacterial growth and spatial movement
- Creators
- Xueying Wang - Department of Mathematics, Washington State UniversityJin Wang - Department of Mathematics, University of Tennessee at Chattanooga
- Publication Details
- Journal of biological dynamics, Vol.9(sup1), pp.233-261
- Academic Unit
- Mathematics and Statistics, Department of
- Publisher
- Taylor & Francis
- Identifiers
- 99900546700601842
- Language
- English
- Resource Type
- Journal article