A Modified SIR Model Used to Investigate the Relationship Between Congenital and Adult Syphilis

Author

Kaleesta R. Waysman, University of South DakotaFollow

Date of Award

Spring 5-10-2025

Document Type

Honors Thesis

Department/Major

Biology

Additional Department

Mathematics

First Advisor

Dan Van Peursem

Second Advisor

Jacob Kerby

Third Advisor

Kevin O'Callaghan

Keywords

Congenital Syphilis, Syphilis, Clinical Sequelae, Mathematical Model, Epidemiology

Subject Categories

Bacteria | Bacterial Infections and Mycoses | Community Health and Preventive Medicine | Disease Modeling | Female Urogenital Diseases and Pregnancy Complications | Infectious Disease | Maternal and Child Health | Partial Differential Equations

Abstract

A complex SIR model integrating the relationship between adult and congenital syphilis was developed. The goal of the project was to determine the specific population(s) or control strategies that should be enforced, altered, or removed to decrease the number of children experiencing clinical sequelae due to congenital syphilis. Early clinical sequelae include hydrops fetalis, preterm birth, central nervous system infection, hepatosplenomegaly, hyperbilirubinemia, cholestasis, hemolytic anemia, snuffles, osteochondritis, and lesions or rashes in the palms and soles. Late clinical sequelae include interstitial keratitis, hearing loss, Hutchinson teeth, saber shins, Clutton joints, mulberry molars, and saddle nose. After implementing real-world data into the SIR model, differential equations, steady state equilibria (disease-present and disease-free), and a steady state graph were analyzed. The stability of the model was determined via Jacobian matrices and resulting eigenvalues. The model was found to be unstable, significantly relying on initial condition values. Then, a sensitivity analysis testing the effect of all relevant parameters on L(t) was conducted. When the parameters representing the transmission rate and sexual activity rate (β and ε, respectively) were increased or decreased by 20%, the number of children experiencing clinical sequelae due to congenital syphilis was impacted most significantly. Thus, our results conclude that our preventative efforts should be directed toward the susceptible, high-risk populations.

Recommended Citation

Waysman, Kaleesta R., "A Modified SIR Model Used to Investigate the Relationship Between Congenital and Adult Syphilis" (2025). Honors Thesis. 381.
https://red.library.usd.edu/honors-thesis/381