Positivity and Boundedness Preserving Numerical Scheme for a Stochastic Multigroup Susceptible-Infected-Recovering...

Area of Science:

• Epidemiology
• Computational Mathematics
• Mathematical Biology

Background:

• Stochastic age-structured multigroup SIR models are nonlinear, making explicit solutions difficult.
• Predicting infection numbers requires effective numerical methods.
• These models exhibit positivity and boundedness properties crucial for realistic simulations.

Purpose of the Study:

• To develop a numerical method that preserves the positivity and boundedness of solutions for stochastic age-structured multigroup SIR models.
• To ensure numerical solutions share essential analytical properties.
• To provide a reliable tool for predicting infection dynamics.

Main Methods:

• Modification of the classical Euler-Maruyama (EM) scheme to create a positivity and boundedness preserving EM (PBPEM) method.
• Development of a full-discrete scheme by integrating the PBPEM method with the finite element method.
• Analysis of strong convergence and error estimations for the proposed schemes.

Main Results:

• The PBPEM method is proven to have strong convergence to the true solution over finite time intervals.
• The full-discrete scheme accurately represents numerical solutions.
• Error estimations for the full-discrete scheme were analyzed.

Conclusions:

• The developed full-discrete scheme, combining PBPEM and finite element methods, is superior for simulating stochastic age-structured multigroup SIR models.
• The method demonstrates effectiveness when applied to general stochastic two-group SIR and Chlamydia epidemic models.
• This approach enhances the reliability of epidemic modeling and prediction.