Mathematical Assessment of the Role of Early Latent Infections and Targeted Control Strategies on Syphilis Transmission Dynamics

D. Okuonghae, Abba Gumel, B. O. Ikhimwin, E. Iboi

Research output: Contribution to journalArticle

Abstract

A new multi-stage deterministic model for the transmission dynamics of syphilis, which incorporates disease transmission by individuals in the early latent stage of syphilis infection and the reversions of early latent syphilis to the primary and secondary stages, is formulated and rigorously analysed. The model is used to assess the population-level impact of preventive (condom use) and therapeutic measures (treatment using antibiotics) against the spread of the disease in a community. It is shown that the disease-free equilibrium of the model is globally-asymptotically stable whenever the associated control reproduction number (denoted by (Formula presented.)) is less than unity. A special case of the model is shown to have a unique and globally-asymptotically stable endemic equilibrium whenever the associated reproduction number (denoted by (Formula presented.)) exceeds unity. Uncertainty and sensitivity analysis of the model, using parameter values and ranges relevant to syphilis transmission dynamics in Nigeria, show that the top three parameters that drive the syphilis infection (with respect to (Formula presented.)) are the disease transmission rate ((Formula presented.)), compliance in condom use (c) and efficacy of condom ((Formula presented.)). Numerical simulations of the model show that the targeted treatment of secondary syphilis cases is more effective than the targeted treatment of individuals in the primary or early latent stage of syphilis infection.

Original languageEnglish (US)
Pages (from-to)1-38
Number of pages38
JournalActa Biotheoretica
DOIs
StateAccepted/In press - Jul 3 2018

Fingerprint

syphilis
Latent Syphilis
Syphilis
Infection Control
Infection
Control Strategy
Condoms
Reproduction number
infection
Globally Asymptotically Stable
Reproduction
disease transmission
condom use
Multistage Model
Therapeutic Uses
Nigeria
Uncertainty Analysis
Model
Endemic Equilibrium
Compliance

Keywords

  • Early latency
  • Global stability
  • Mathematical model
  • Syphilis
  • Targeted control
  • Uncertainty and sensitivity analysis

ASJC Scopus subject areas

  • Biochemistry, Genetics and Molecular Biology(all)
  • Philosophy
  • Environmental Science(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics

Cite this

Mathematical Assessment of the Role of Early Latent Infections and Targeted Control Strategies on Syphilis Transmission Dynamics. / Okuonghae, D.; Gumel, Abba; Ikhimwin, B. O.; Iboi, E.

In: Acta Biotheoretica, 03.07.2018, p. 1-38.

Research output: Contribution to journalArticle

@article{60d065349d544f75984137ef73d277fb,
title = "Mathematical Assessment of the Role of Early Latent Infections and Targeted Control Strategies on Syphilis Transmission Dynamics",
abstract = "A new multi-stage deterministic model for the transmission dynamics of syphilis, which incorporates disease transmission by individuals in the early latent stage of syphilis infection and the reversions of early latent syphilis to the primary and secondary stages, is formulated and rigorously analysed. The model is used to assess the population-level impact of preventive (condom use) and therapeutic measures (treatment using antibiotics) against the spread of the disease in a community. It is shown that the disease-free equilibrium of the model is globally-asymptotically stable whenever the associated control reproduction number (denoted by (Formula presented.)) is less than unity. A special case of the model is shown to have a unique and globally-asymptotically stable endemic equilibrium whenever the associated reproduction number (denoted by (Formula presented.)) exceeds unity. Uncertainty and sensitivity analysis of the model, using parameter values and ranges relevant to syphilis transmission dynamics in Nigeria, show that the top three parameters that drive the syphilis infection (with respect to (Formula presented.)) are the disease transmission rate ((Formula presented.)), compliance in condom use (c) and efficacy of condom ((Formula presented.)). Numerical simulations of the model show that the targeted treatment of secondary syphilis cases is more effective than the targeted treatment of individuals in the primary or early latent stage of syphilis infection.",
keywords = "Early latency, Global stability, Mathematical model, Syphilis, Targeted control, Uncertainty and sensitivity analysis",
author = "D. Okuonghae and Abba Gumel and Ikhimwin, {B. O.} and E. Iboi",
year = "2018",
month = "7",
day = "3",
doi = "10.1007/s10441-018-9336-9",
language = "English (US)",
pages = "1--38",
journal = "Acta Biotheoretica",
issn = "0001-5342",
publisher = "Springer Netherlands",

}

TY - JOUR

T1 - Mathematical Assessment of the Role of Early Latent Infections and Targeted Control Strategies on Syphilis Transmission Dynamics

AU - Okuonghae, D.

AU - Gumel, Abba

AU - Ikhimwin, B. O.

AU - Iboi, E.

PY - 2018/7/3

Y1 - 2018/7/3

N2 - A new multi-stage deterministic model for the transmission dynamics of syphilis, which incorporates disease transmission by individuals in the early latent stage of syphilis infection and the reversions of early latent syphilis to the primary and secondary stages, is formulated and rigorously analysed. The model is used to assess the population-level impact of preventive (condom use) and therapeutic measures (treatment using antibiotics) against the spread of the disease in a community. It is shown that the disease-free equilibrium of the model is globally-asymptotically stable whenever the associated control reproduction number (denoted by (Formula presented.)) is less than unity. A special case of the model is shown to have a unique and globally-asymptotically stable endemic equilibrium whenever the associated reproduction number (denoted by (Formula presented.)) exceeds unity. Uncertainty and sensitivity analysis of the model, using parameter values and ranges relevant to syphilis transmission dynamics in Nigeria, show that the top three parameters that drive the syphilis infection (with respect to (Formula presented.)) are the disease transmission rate ((Formula presented.)), compliance in condom use (c) and efficacy of condom ((Formula presented.)). Numerical simulations of the model show that the targeted treatment of secondary syphilis cases is more effective than the targeted treatment of individuals in the primary or early latent stage of syphilis infection.

AB - A new multi-stage deterministic model for the transmission dynamics of syphilis, which incorporates disease transmission by individuals in the early latent stage of syphilis infection and the reversions of early latent syphilis to the primary and secondary stages, is formulated and rigorously analysed. The model is used to assess the population-level impact of preventive (condom use) and therapeutic measures (treatment using antibiotics) against the spread of the disease in a community. It is shown that the disease-free equilibrium of the model is globally-asymptotically stable whenever the associated control reproduction number (denoted by (Formula presented.)) is less than unity. A special case of the model is shown to have a unique and globally-asymptotically stable endemic equilibrium whenever the associated reproduction number (denoted by (Formula presented.)) exceeds unity. Uncertainty and sensitivity analysis of the model, using parameter values and ranges relevant to syphilis transmission dynamics in Nigeria, show that the top three parameters that drive the syphilis infection (with respect to (Formula presented.)) are the disease transmission rate ((Formula presented.)), compliance in condom use (c) and efficacy of condom ((Formula presented.)). Numerical simulations of the model show that the targeted treatment of secondary syphilis cases is more effective than the targeted treatment of individuals in the primary or early latent stage of syphilis infection.

KW - Early latency

KW - Global stability

KW - Mathematical model

KW - Syphilis

KW - Targeted control

KW - Uncertainty and sensitivity analysis

UR - http://www.scopus.com/inward/record.url?scp=85049565500&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85049565500&partnerID=8YFLogxK

U2 - 10.1007/s10441-018-9336-9

DO - 10.1007/s10441-018-9336-9

M3 - Article

SP - 1

EP - 38

JO - Acta Biotheoretica

JF - Acta Biotheoretica

SN - 0001-5342

ER -