A mathematical study of a model for childhood diseases with non-permanent immunity

S. M. Moghadas, Abba Gumel

Research output: Contribution to journalArticle

33 Citations (Scopus)

Abstract

Protecting children from diseases that can be prevented by vaccination is a primary goal of health administrators. Since vaccination is considered to be the most effective strategy against childhood diseases, the development of a framework that would predict the optimal vaccine coverage level needed to prevent the spread of these diseases is crucial. This paper provides this framework via qualitative and quantitative analysis of a deterministic mathematical model for the transmission dynamics of a childhood disease in the presence of a preventive vaccine that may wane over time. Using global stability analysis of the model, based on constructing a Lyapunov function, it is shown that the disease can be eradicated from the population if the vaccination coverage level exceeds a certain threshold value. It is also shown that the disease will persist within the population if the coverage level is below this threshold. These results are verified numerically by constructing, and then simulating, a robust semi-explicit second-order finite-difference method.

Original languageEnglish (US)
Pages (from-to)347-363
Number of pages17
JournalJournal of Computational and Applied Mathematics
Volume157
Issue number2
DOIs
StatePublished - Aug 15 2003
Externally publishedYes

Fingerprint

Immunity
Vaccination
Coverage
Vaccines
Vaccine
Model
Global Analysis
Deterministic Model
Qualitative Analysis
Lyapunov functions
Global Stability
Threshold Value
Quantitative Analysis
Finite difference method
Lyapunov Function
Difference Method
Stability Analysis
Finite Difference
Exceed
Health

Keywords

  • Basic reproductive number
  • Epidemic models
  • Equilibria
  • Finite-difference method
  • Stability
  • Vaccination

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

Cite this

A mathematical study of a model for childhood diseases with non-permanent immunity. / Moghadas, S. M.; Gumel, Abba.

In: Journal of Computational and Applied Mathematics, Vol. 157, No. 2, 15.08.2003, p. 347-363.

Research output: Contribution to journalArticle

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