Breakdown of a Nonlinear Stochastic Nipah Virus Epidemic Models through Efficient Numerical Methods.

Area of Science:

• Epidemiology
• Mathematical Biology
• Computational Science

Background:

• Nipah virus (NiV) is a zoonotic pathogen with high fatality rates (40-75%), posing a significant public health threat.
• Transmission occurs through animals, contaminated food, and human-to-human contact, with outbreaks reported in several Asian countries.
• NiV modeling typically uses susceptible-exposed-infected-recovered (SEIR) frameworks.

Purpose of the Study:

• To develop and evaluate a novel numerical method for simulating Nipah virus dynamics.
• To address the limitations of existing stochastic methods in accurately capturing biological model properties.
• To introduce a computationally efficient and stable approach for epidemiological modeling.

Main Methods:

• The study proposes a stochastic non-standard finite difference (NSFD) method.
• This approach integrates standard and non-standard numerical techniques.
• Key properties evaluated include dynamical consistency, positivity, and boundedness.

Main Results:

• The stochastic NSFD method demonstrates stability and convergence across all time steps.
• In contrast, traditional methods like Euler-Maruyama and Stochastic Runge-Kutta show conditional convergence or long-term divergence.
• The NSFD method provides efficient and low-cost approximations while maintaining essential model characteristics.

Conclusions:

• The stochastic NSFD method is an efficient and cost-effective numerical technique for NiV modeling.
• It successfully preserves crucial properties like positivity and boundedness, ensuring reliable simulations.
• This method offers a superior alternative to existing stochastic approaches for epidemiological studies.