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Zbl 1139.92017
Alexander, Murray E.; Moghadas, Seyed M.; Röst, Gergely; Wu, Jianhong
A delay differential model for pandemic influenza with antiviral treatment. (English)
[J] Bull. Math. Biol. 70, No. 2, 382-397 (2008). ISSN 0092-8240; ISSN 1522-9602/e

Summary: The use of antiviral drugs has been recognized as the primary public health strategy for mitigating the severity of a new influenza pandemic strain. However, the success of this strategy requires the prompt onset of therapy within 48 hours of the appearance of clinical symptoms. This requirement may be captured by a compartmental model that monitors the density of infected individuals in terms of the time elapsed since the onset of symptoms. We show that such a model can be expressed by a system of delay differential equations with both discrete and distributed delays. The model is analyzed to derive the criterion for disease control based on two critical factors: (i) the profile of treatment rate; and (ii) the level of treatment as a function of time lag in commencing therapy. Numerical results are also obtained to illustrate the feasible region of disease control. Our findings show that due to uncertainty in the attack rate of a pandemic strain, initiating therapy immediately upon diagnosis can significantly increase the likelihood of disease control and substantially reduce the required community-level of treatment. This suggests that reliable diagnostic methods for influenza cases should be rapidly implemented within an antiviral treatment strategy.

MSC 2000:: *92C60 Medical epidemiology
34K60 Applications of functional-differential equations
34K35 Functional-differential equations connected with control problems
92C50 Medical appl. of mathematical biology
93A30 Mathematical modelling of systems

Keywords: delay equations; epidemic model

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