A Mathematical Model Illustrating the Dynamics of At‐Risk Lumbar Disc Herniated Population With Conceptual Standard Incidence

Lumbar disc herniation (LDH) is a widespread health problem, which is a reason for lower back pain. Poor ergonomics, obesity, modern sedentary lifestyles, a history of cesarean delivery, and vitamin D deficiency are included as key risk factors that can lead to nerve compression and result in radicular or sciatic pain. An incidence of 5–20 cases per 1000 individuals is recognized as an LDH problem in the United States (US) annually. This motivates the development of a nonlinear compartmental model to examine long‐term disease dynamics over a 50‐year horizon. A four‐compartment mathematical model is formulated that includes individuals with a healthy spine, radicular or sciatic pain, affected intervertebral discs, and a recovered class population. The model of LDH is governed by balance principles with conceptual standard incidence and analyzed through positivity, boundedness, equilibrium points, stability analysis, and the basic progression number, with parameters adjusted from US healthcare data. The stability of the LDH model is determined by the basic progression number. The stability of the disease‐free equilibrium and key factors are recognized through simulations of LDH progression. This model will be useful for predicting future disease dynamics and disease origin. Numerical simulations capture the factors of disease progression and factors of disease prevention. This study has applications in both medical and social disciplines.