Modeling Rabies Transmission in Spatially Heterogeneous Environments via $$\theta $$-diffusion
- 12 January 2021
- journal article
- research article
- Published by Springer Science and Business Media LLC in Bulletin of Mathematical Biology
- Vol. 83 (2), 1-38
- https://doi.org/10.1007/s11538-020-00857-1
Abstract
Rabies among dogs remains a considerable risk to humans and constitutes a serious public health concern in many parts of the world. Conventional mathematical models for rabies typically assume homogeneous environments, with a standard diffusion term for the population of rabid animals. It has recently been recognized, however, that spatial heterogeneity plays an important role in determining spatial patterns of rabies and the cost-effectiveness of vaccinations. In this paper, we develop a spatially heterogeneous dog rabies model by using the \(\theta \)-diffusion equation, where \(\theta \) reflects the way individual dogs make movement decisions in the underlying random walk. We numerically investigate the dynamics of the model in three diffusion cases: homogeneous, city-wild, and Gaussian-type. We find that the initial conditions affect whether traveling waves or epizootic waves can be observed. However, different initial conditions have little impact on steady-state solutions. An “active” interface is observed between city and wild regions, with a “ridge” on the city side and a “valley” on the wild side for the infectious dog population. In addition, the progressing speed of epizootic waves changes in heterogeneous environments. It is impossible to eliminate rabies in the entire spatial domain if vaccination is focused only in the city region or only in the wild region. When a seasonal transmission is incorporated, the dog population size approaches a positive time-periodic spatially heterogeneous state eventually.
Keywords
Funding Information
- IUSEP
- NSERC Discovery Grant (RGPIN-2020-03911)
- NSERC Accelerator Grant (RGPAS-2020-00090)
- NSERC (RGPIN 05395 Li)
This publication has 25 references indexed in Scilit:
- Host and viral ecology determine bat rabies seasonality and maintenanceProceedings of the National Academy of Sciences, 2011
- Optimal vaccine distribution in a spatiotemporal epidemic model with an application to rabies and raccoonsJournal of Mathematical Analysis and Applications, 2011
- Mathematical Models for RabiesPublished by Elsevier BV ,2011
- Transmission dynamics and economics of rabies control in dogs and humans in an African cityProceedings of the National Academy of Sciences, 2009
- Synchronous cycles of domestic dog rabies in sub-Saharan Africa and the impact of control effortsProceedings of the National Academy of Sciences of the United States of America, 2007
- Modelling wildlife rabies: Transmission, economics, and conservationBiological Conservation, 2006
- Spatial Spread of Rabies Revisited: Influence of Age‐Dependent Diffusion on Nonlinear DynamicsSIAM Journal on Applied Mathematics, 2006
- Discrete-time deterministic and stochastic models for the spread of rabiesApplied Mathematics and Computation, 2002
- A simple model for the spatial spread and control of rabiesJournal of Theoretical Biology, 1985
- Population dynamics of fox rabies in EuropeNature, 1981