Competitive analysis for stochastic influenza model with constant vaccination strategy

Area of Science:

• Mathematical epidemiology
• Computational modeling
• Public health dynamics

Background:

• Deterministic models simplify disease spread, potentially missing crucial real-world dynamics.
• Stochastic models offer a more pragmatic approach to influenza transmission, incorporating inherent randomness.
• Understanding disease persistence and control hinges on accurate epidemiological parameters.

Purpose of the Study:

• To perform a competitive analysis between stochastic and deterministic influenza models.
• To investigate the impact of the influenza generation number on disease control and endemicity.
• To evaluate a novel stochastic influenza model using a non-standard finite difference scheme.

Main Methods:

• Comparative analysis of stochastic and deterministic influenza models.
• Development and application of a stochastic influenza model.
• Implementation using a stochastic non-standard finite difference scheme.
• Analysis of the influenza generation number's effect on disease dynamics.

Main Results:

• Stochastic influenza models provide a more pragmatic representation of disease spread compared to deterministic models.
• The influenza generation number is a critical threshold: <1 suggests control, >1 suggests endemic persistence.
• The proposed stochastic non-standard finite difference scheme preserves essential model characteristics like positivity and boundedness.

Conclusions:

• Stochastic modeling is superior for analyzing influenza dynamics and control strategies.
• The influenza generation number is a vital metric for predicting disease outcomes.
• The developed numerical scheme ensures the reliability and validity of the stochastic influenza model.