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The Ross-Macdonald model in a patchy environment
Pierre Auger1, Etienne Kouokam, Gauthier Sallet
1IRD, UR GEODES, 32 Avenue Henri Varagnat, 3143 Bondy Cedex, France.
Mathematical Biosciences
|September 23, 2008
Summary
This study extends the Ross-Macdonald model for malaria dynamics to n patches, including vector-free areas. It proves that if the basic reproduction number (R0) is less than 1, the disease disappears; otherwise, a stable endemic state emerges.
Area of Science:
- Epidemiology
- Mathematical Biology
- Vector-borne Disease Dynamics
Background:
- The Ross-Macdonald model is a foundational framework for understanding malaria transmission dynamics.
- Previous models often assumed uniform conditions across all environments, neglecting spatial heterogeneity.
- The impact of vector-free zones and host migration on disease persistence requires further investigation.
Purpose of the Study:
- To generalize the Ross-Macdonald model to an n-patch system incorporating vector-free areas.
- To analyze the influence of host migration on malaria transmission patterns.
- To determine the conditions for disease eradication versus endemic persistence in a heterogeneous environment.
Main Methods:
- Development of a compartmental mathematical model for n-patch malaria dynamics.
- Inclusion of host migration between patches with identical dispersal rates for susceptible and infectious individuals.
- Analysis of the basic reproduction number (R0) and stability of equilibrium points.
Main Results:
- The basic reproduction number (R0) was computed for the n-patch model.
- Global asymptotic stability of the disease-free equilibrium was proven when R0 < 1.
- Existence and global asymptotic stability of a unique endemic equilibrium were demonstrated when R0 > 1.
Conclusions:
- The generalized n-patch model provides a more realistic representation of malaria transmission in heterogeneous landscapes.
- Host migration plays a crucial role in disease spread and persistence.
- The critical threshold R0 effectively predicts disease eradication or endemicity in complex spatial settings.
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