A reaction–diffusion malaria model with incubation period in the vector population
Top Cited Papers
- 30 April 2010
- journal article
- research article
- Published by Springer Science and Business Media LLC in Journal of Mathematical Biology
- Vol. 62 (4), 543-568
- https://doi.org/10.1007/s00285-010-0346-8
Abstract
Malaria is one of the most important parasitic infections in humans and more than two billion people are at risk every year. To understand how the spatial heterogeneity and extrinsic incubation period (EIP) of the parasite within the mosquito affect the dynamics of malaria epidemiology, we propose a nonlocal and time-delayed reaction–diffusion model. We then define the basic reproduction ratio \({\mathcal{R}_0}\) and show that \({\mathcal{R}_0}\) serves as a threshold parameter that predicts whether malaria will spread. Furthermore, a sufficient condition is obtained to guarantee that the disease will stabilize at a positive steady state eventually in the case where all the parameters are spatially independent. Numerically, we show that the use of the spatially averaged system may highly underestimate the malaria risk. The spatially heterogeneous framework in this paper can be used to design the spatial allocation of control resources.
Keywords
This publication has 28 references indexed in Scilit:
- The effects of human movement on the persistence of vector-borne diseasesJournal of Theoretical Biology, 2009
- An age-structured model to evaluate the potential of novel malaria-control interventions: a case study of fungal biopesticide spraysProceedings. Biological sciences, 2008
- On the Delayed Ross–Macdonald Model for Malaria TransmissionBulletin of Mathematical Biology, 2008
- Transmission assumptions generate conflicting predictions in host–vector disease models: a case study in West Nile virusEcology Letters, 2006
- Global traffic and disease vector dispersalProceedings of the National Academy of Sciences of the United States of America, 2006
- Perspectives on the basic reproductive ratioJournal of The Royal Society Interface, 2005
- The global distribution of clinical episodes of Plasmodium falciparum malariaNature, 2005
- Global Attractors and Steady States for Uniformly Persistent Dynamical SystemsSIAM Journal on Mathematical Analysis, 2005
- The Risk of a Mosquito-Borne Infectionin a Heterogeneous EnvironmentPLoS Biology, 2004
- Robust persistence for semidynamical systemsNonlinear Analysis, 2001