A model for influenza with vaccination and antiviral treatment.

Compartmental models for influenza that include control by vaccination and antiviral treatment are formulated. Analytic expressions for the basic reproduction number, control reproduction number and the final size of the epidemic are derived for this general class of disease transmission models. Sensitivity and uncertainty analyses of the dependence of the control reproduction number on the parameters of the model give a comparison of the various intervention strategies. Numerical computations of the deterministic models are compared with those of recent stochastic simulation influenza models. Predictions of the deterministic compartmental models are in general agreement with those of the stochastic simulation models.

[1]  O. Diekmann.  Mathematical Epidemiology of Infectious Diseases , 1996 .

[2]  A. Nizam,et al.  Containing Pandemic Influenza at the Source , 2005, Science.

[3]  Alessandro Vespignani,et al.  Modeling the Worldwide Spread of Pandemic Influenza: Baseline Case and Containment Interventions , 2007, PLoS medicine.

[4]  A. Nizam,et al.  Containing pandemic influenza with antiviral agents. , 2004, American journal of epidemiology.

[5]  J. Watmough,et al.  Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. , 2002, Mathematical biosciences.

[6]  Jodie McVernon,et al.  Prophylaxis or treatment? Optimal use of an antiviral stockpile during an influenza pandemic. , 2007, Mathematical biosciences.

[7]  Nadav Davidovitch,et al.  Cost-Benefit of Stockpiling Drugs for Influenza Pandemic , 2005, Emerging infectious diseases.

[8]  Ping Yan,et al.  Emergence of drug resistance: implications for antiviral control of pandemic influenza , 2007, Proceedings of the Royal Society B: Biological Sciences.

[9]  M. E. Alexander,et al.  Modelling strategies for controlling SARS outbreaks , 2004, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[10]  J. Robins,et al.  Transmission Dynamics and Control of Severe Acute Respiratory Syndrome , 2003, Science.

[11]  D. Cummings,et al.  Strategies for containing an emerging influenza pandemic in Southeast Asia , 2005, Nature.

[12]  Fred Brauer,et al.  Some simple epidemic models. , 2005, Mathematical biosciences and engineering : MBE.

[13]  Julien Arino,et al.  A final size relation for epidemic models. , 2007, Mathematical biosciences and engineering : MBE.

[14]  C. Fraser,et al.  Reducing the impact of the next influenza pandemic using household-based public health interventions. , 2006, Hong Kong medical journal = Xianggang yi xue za zhi.

[15]  F. Brauer,et al.  Simple models for containment of a pandemic , 2006, Journal of The Royal Society Interface.

[16]  Steve Leach,et al.  Potential Impact of Antiviral Drug Use during Influenza Pandemic , 2005, Emerging infectious diseases.