Analysis, control, and forecasting the dynamics of SIRD models with saturated treatment and nonlinear incidence

Clinical Snapshot

Key Findings

• Effect Size: Not applicable - theoretical model

• Primary Outcome: Mathematical characterisation of epidemic dynamics with identification of transcritical, saddle-node, and Hopf bifurcations

• Nnt Or Sensitivity: Machine learning forecasting accuracy not quantified with specific metrics

• Confidence Interval: Not provided

Clinical Application

High computational requirements for real-time implementation; requires expertise in mathematical modelling and machine learning Could inform Australian Department of Health epidemic preparedness strategies, but would need validation against Australian epidemiological data and integration with existing surveillance systems Theoretical framework applicable to any epidemic scenario but requires calibration for specific populations and diseases

Abstract

This study addresses the challenge of managing complex epidemic dynamics exhibited by a novel Susceptible-Infected-Recovered-Deceased (SIRD) model. The introduced model incorporates a biologically and behaviorally mediated nonlinear incidence rate alongside a saturated treatment function, realistically capturing both physical transmission risks and the human behavioral responses during an outbreak. Our comprehensive analysis establishes the mathematical rigor of the system through positivity, boundedness, and a detailed investigation of equilibrium points and bifurcations (transcritical, saddle-node, and Hopf), which reveal the potential for complex, oscillatory, and chaotic epidemic patterns. To mitigate the disease burden, we apply Pontryagin's Maximum Principle to derive optimal time-dependent prevention and treatment control strategies. Furthermore, we introduce a highly efficient machine learning framework based on a Logistic-Map Reservoir Computer (LMRC) for accurate, real-time forecasting of these complex dynamics. Numerical simulations validate the theoretical findings and reveal the model's rich dynamical behaviors, including stable limit cycles and chaotic regimes driven by parameter variations. The integrated analytical, control, and machine learning approach provides a robust toolkit for public health policymakers, offering data-driven insights crucial for designing adaptive, cost-effective interventions that directly support the achievement of Sustainable Development Goal 3 (Good Health and Well-being).

References

1. 1.Elsonbaty, A., Ramaswamy, R., Padmaja, S., Teklu, S. W., Abdelkawy, M. A., & El-Mesady, A. (2026). Analysis, control, and forecasting the dynamics of SIRD models with saturated treatment and nonlinear incidence. Scientific Reports. https://doi.org/10.1016/j.chaos.2023.113775