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Jpn J Ind Appl Math. 2016;33(1):269-296. doi: 10.1007/s13160-016-0210-3. Epub 2016 Jan 21.
Mathematical analysis of swine influenza epidemic model with optimal control.
Imran M[SUP]1[/SUP], Malik T[SUP]2[/SUP], Ansari AR[SUP]1[/SUP], Khan A[SUP]3[/SUP].
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Abstract
A deterministic model is designed and used to analyze the transmission dynamics and the impact of antiviral drugs in controlling the spread of the 2009 swine influenza pandemic. In particular, the model considers the administration of the antiviral both as a preventive as well as a therapeutic agent. Rigorous analysis of the model reveals that its disease-free equilibrium is globally asymptotically stable under a condition involving the threshold quantity-reproduction number [FONT=MathJax_Math]R[/FONT][FONT=MathJax_Math]c[/FONT] . The disease persists uniformly if [FONT=MathJax_Math]R[/FONT][FONT=MathJax_Math]c[/FONT][FONT=MathJax_Main]>[/FONT][FONT=MathJax_Main]1[/FONT] and the model has a unique endemic equilibrium under certain condition. The model undergoes backward bifurcation if the antiviral drugs are completely efficient. Uncertainty and sensitivity analysis is presented to identify and study the impact of critical model parameters on the reproduction number. A time dependent optimal treatment strategy is designed using Pontryagin's maximum principle to minimize the treatment cost and the infected population. Finally the reproduction number is estimated for the influenza outbreak and model provides a reasonable fit to the observed swine (H1N1) pandemic data in Manitoba, Canada, in 2009.
? The JJIAM Publishing Committee and Springer Japan 2016.
KEYWORDS:
Backward bifurcation; Influenza; Optimal control; Reproduction number; Statistical inference; Uncertainty and sensitivity analysis
PMID:32226225PMCID:PMC7097131DOI:10.1007/s13160-016-0210-3
Free PMC Article
Mathematical analysis of swine influenza epidemic model with optimal control.
Imran M[SUP]1[/SUP], Malik T[SUP]2[/SUP], Ansari AR[SUP]1[/SUP], Khan A[SUP]3[/SUP].
Author information
Abstract
A deterministic model is designed and used to analyze the transmission dynamics and the impact of antiviral drugs in controlling the spread of the 2009 swine influenza pandemic. In particular, the model considers the administration of the antiviral both as a preventive as well as a therapeutic agent. Rigorous analysis of the model reveals that its disease-free equilibrium is globally asymptotically stable under a condition involving the threshold quantity-reproduction number [FONT=MathJax_Math]R[/FONT][FONT=MathJax_Math]c[/FONT] . The disease persists uniformly if [FONT=MathJax_Math]R[/FONT][FONT=MathJax_Math]c[/FONT][FONT=MathJax_Main]>[/FONT][FONT=MathJax_Main]1[/FONT] and the model has a unique endemic equilibrium under certain condition. The model undergoes backward bifurcation if the antiviral drugs are completely efficient. Uncertainty and sensitivity analysis is presented to identify and study the impact of critical model parameters on the reproduction number. A time dependent optimal treatment strategy is designed using Pontryagin's maximum principle to minimize the treatment cost and the infected population. Finally the reproduction number is estimated for the influenza outbreak and model provides a reasonable fit to the observed swine (H1N1) pandemic data in Manitoba, Canada, in 2009.
? The JJIAM Publishing Committee and Springer Japan 2016.
KEYWORDS:
Backward bifurcation; Influenza; Optimal control; Reproduction number; Statistical inference; Uncertainty and sensitivity analysis
PMID:32226225PMCID:PMC7097131DOI:10.1007/s13160-016-0210-3
Free PMC Article