Mathematical Model for Curtailing Neurosyphilis Through Early Treatment

Abstract

Syphilis, caused by Treponema pallidum, remains a major global health burden with millions of new cases annually and severe complications, including neurosyphilis, if left untreated. This study develops an eight-compartment deterministic ODE model to examine syphilis transmission dynamics and quantify the effect of early treatment in preventing progression to neurosyphilis. The model incorporates susceptible, primary, secondary, latent, treated (early), recovered, neurosyphilis, and treated-neurosyphilis compartments. The disease-free equilibrium (DFE) is shown to be locally asymptotically stable by Jacobian analysis and globally asymptotically stable via the Castillo-Chavez framework when R₀ < 1. Global stability of the endemic equilibrium when R₀ > 1 is established using a Lyapunov function. The basic reproduction number, computed via the next-generation matrix method, yields R₀ = 0.09975 under baseline parameters (𝜇 = 0.0143/year), confirming disease-free conditions under current treatment coverage. Sensitivity analysis identifies the primary treatment rate 𝛽₁ (index −0.5566) and primary infectivity 𝜂₁ (index +0.6984) as the most influential parameters. Numerical simulations confirm that scaling-up early treatment dramatically reduces neurosyphilis incidence. Model limitations and future extensions are discussed.

Received: 24 April 2026 | Revised: 30 July 2026 | Accepted: 3 September 2026

Conflicts of Interest

The authors declare that they have no conflicts of interest to this work.

Data Availability Statement

No new data were generated or analyzed in this study. All parameter values required to reproduce the results are provided within the manuscript (Table 2), sourced from publicly available peer-reviewed publications and surveillance reports cited in the reference list.

Author Contribution Statement

Nita H. Shah: Conceptualization, Methodology, Validation, Formal analysis, Investigation, Writing – original draft, Writing –review & editing, Visualization, Supervision, Project administration. Jalpa N. Vaghela: Methodology, Software, Validation, Formal analysis, Investigation, Resources, Writing – original draft, Writing – review & editing, Visualization. Yash N. Shah: Conceptualization, Investigation, Data curation, Writing – review & editing, Visualization.