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This study introduces a new stochastic model for vector-borne diseases (VBDs), simplifying complex dynamics for better analysis. Findings show VBD spread depends on a basic reproduction number (R0) and population scaling.

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Fast and slow dynamicsFunctional central limit theoremFunctional law of large numbersMultiscale analysisQuasi-stationary distributionsSIS compartment modelTime to extinctionVector-borne disease model

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Vector-Borne Diseases

Background:

  • Stochastic epidemic models offer greater realism than deterministic ones but are often too complex for analysis.
  • Vector-borne diseases (VBDs) present increased complexity due to pathogen transmission via arthropod vectors.
  • Analyzing VBD dynamics requires accounting for demographical, ecological, and social factors across different host and vector scales.

Purpose of the Study:

  • To develop a stochastic vector-borne disease (VBD) model incorporating realistic transmission features.
  • To introduce and evaluate novel mathematical methods for systematic analysis of complex VBD dynamics.
  • To understand how demographical, ecological, social mechanisms, and host/vector scales influence VBD transmission.

Main Methods:

  • Development of a novel stochastic VBD model.
  • Application of dimensional reduction and model simplification techniques using scaling limit theorems.
  • Utilizing simulations for specific parameter scenarios to validate analytical findings.

Main Results:

  • Stochastic VBD dynamics are influenced by the basic reproduction number (R0), initial infective population size, and host population scaling.
  • R0 acts as a critical threshold for infection persistence, consistent with other infectious disease models.
  • Faster vector dynamics can simplify the model by averaging out effects, significantly reducing its dimensionality.

Conclusions:

  • The developed mathematical framework provides a robust method for analyzing complex stochastic VBD models.
  • Understanding the interplay of R0, initial conditions, and population scaling is crucial for predicting VBD spread.
  • Model simplification through scaling, especially with rapid vector dynamics, offers a pathway to more tractable analyses of VBD transmission.