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Research
Potential Impact of Antiviral
Use on Hospitalizations during Influenza Pandemic
Raymond Gani,*
Helen Hughes,* Douglas Fleming,† Thomas Griffin,* Jolyon Medlock,* and
Steve Leach*
*Health Protection Agency, Salisbury, Wiltshire, United Kingdom; and †Royal
College of General Practitioners, Harborne, Birmingham, United Kingdom
Appendix: Mathematical Model
Used To Calculate Outputs
The model used was based on Kermack and McKendrick (1),
which has formed the basis of a number of models for both epidemic and
pandemic influenza (2–4) and is implemented by using
the set of differential equations given in equation 1.
 equation
1
where α = 1/L = 0.5, γ = 1/PP = 0.4, λ
= 1/IP = 2/3, and β = R0/(PP + IP). LP represents
the length of the latent period; PP represents the length of the nonsymptomatic
infectious period; and IP represents the length of the infectious symptomatic
period. S represents the total proportion susceptible, E
the total proportion incubating, Pi the proportion from
the total population in each group i within the first 2.5 days
of their infectious period, Ii the proportion of total
population in each group i within the final 1.5 days of their infectious
period, and R the total proportion recovered and immune or dead.
ci is the proportion of infections resulting in clinical
cases, and Ti is the proportion of group i receiving
treatment. The average number of secondary cases per primary case when
the population is entirely susceptible is represented by R0,
and the proportion of the population in each group i
is given by Ni. The proportion treated in each group
each week can be given as Ai(t) as
where t is time in days.
The proportion of the population within each group being hospitalized
each week, Hi(t), can be calculated as
where ε is the efficacy of antiviral treatment against hospitalization
and hi is the hospitalization rate for each group i.
Supplementary information on the probability of hospitalization in the
absence of vaccination is available from the author (see Comments
to the Authors).
Appendix
References
- Kermack WO, McKendrick AG. A contribution to the mathematical
theory of epidemics. Proceedings of the Royal Society A: Mathematical,
Physical and Engineering Sciences. 1927 Series A;115:700–21.
- Rvachev LA, Longini IM. A mathematical model for the global spread
of influenza. Mathematical Biosciences. 1985;75:3–22.
- Flahault A, Letrait S, Blin P, Hazout S, Menares J, Valleron AJ. Modelling
the 1985 influenza epidemic in France. Stat Med. 1988;7:1147–55.
- Flahault A, Deguen S, Valleron AJ. A
mathematical model for the European spread of influenza. Eur J Epidemiol.
1994;10:471–4.
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