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Multiscale analysis for a vector-borne epidemic model.

¹Departamento de Matemática Aplicada, Universidade Federal Fluminense, R. Mário Santos Braga, s/n, Niterói, RJ, 22240-920, Brazil, msouza@mat.uff.br.

Journal of Mathematical Biology

|April 3, 2013

Summary

This summary is machine-generated.

This study simplifies arbovirus disease dynamics by analyzing host and vector time scales. It reveals two distinct models: one for fast host dynamics resembling directly transmitted diseases, and another for fast vector dynamics.

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Area of Science:

Epidemiology
Mathematical Biology
Vector-borne Diseases

Background:

Traditional disease dynamics studies emphasize global stability for epidemiological insights.
Arbovirus transmission involves complex interactions between hosts and vectors.

Purpose of the Study:

To provide an alternative Lyapunov-based proof for known global stability results in SIR-SI models.
To investigate arbovirus dynamics under distinct host and vector intrinsic time scales.

Main Methods:

Lyapunov stability theory for global stability analysis.
Asymptotic analysis to derive reduced models for fast host or fast vector dynamics.
Numerical simulations to validate the reduced models.

Main Results:

A simplified SIR model with rational incidence for fast host dynamics, where vectors are implicitly included.
A simplified SI model for fast vector dynamics, where hosts are implicitly included.
Demonstrated performance of reduced models through numerical results and rigorous proofs.

Conclusions:

Distinct time scales in host-vector systems lead to emergent simplified disease dynamics.
Reduced models offer valuable insights into arbovirus spread under specific temporal assumptions.
The study validates the utility of mathematical modeling in understanding complex epidemiological systems.