A time-domain piecewise PIRNN with algebraic constraints for efficient SITR epidemic modeling

Infectious disease dynamics modeling demands accurate and efficient numerical solvers for nonlinear stiff systems, while traditional compartmental models oversimplify population heterogeneity and intervention effects. To address these issues, this work develops a refined SITR model that distinguishes two susceptible subgroups (S1, S2), infected (I), treated (T), and recovered (R) populations, incorporating natural demography, transmission heterogeneity, and therapeutic interventions. To solve the resulting high-dimensional nonlinear ordinary differential equations, we propose a time-domain piecewise physics-informed random neural network (PIRNN) with algebraic constraints. The method constructs trial functions that exactly satisfy initial conditions, randomly initializes and freezes hidden-weights, and converts the differential system into a set of nonlinear algebraic equations over segmented time subintervals, which are solved sequentially via MATLAB’s fsolve. Compared with the standard physics-informed neural network (PINN), which suffers from slow gradient descent convergence, local minima trapping, and error accumulation in long-time simulations, the proposed PIRNN avoids iterative backpropagation, reduces optimization dimensionality, and mitigates stiffness-induced numerical instability. Numerical experiments on two representative epidemic scenarios demonstrate that the PIRNN achieves 10−8–10−9 level accuracy, significantly outperforming PINN (with errors at 10−3–10−2) and the reference Runge–Kutta (ode45) solver in both solution precision and computational efficiency. The proposed framework provides a robust and scalable tool for dynamic simulation, parameter calibration, and intervention strategy optimization of complex infectious disease systems.