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Vietnam Journal of Mathematics 40:4(2012)
469-495
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A “SE(QF)(IH)R”
Approach to the Introducing
New “Pandemic Threshold” and “Pandemic Estimator”
Parameters for an Infectious Disease
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Omid RabieiMotlagh
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Department
of Applied Mathematics, University of Birjand, Birjand, Iran
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Received October 10,
2011
Revised January 29,
2012
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Abstract. Using the concept of SIR... systems, we
construct the “SE(QF)(IH)R”
system which simulates patterns of the pandemic by an infectious disease.
This system helps us to introduce new “Pandemic Threshold” and “Pandemic
Estimator” parameters. We see that these newly defined parameters forecast
patterns of the pandemic by the disease. We also show that the “SE(QF)(IH)R” system contains two
sub-systems such that local bifurcations of these subsystems cause local
bifurcations of the “SE(QF)(IH)R”
system. This especially occurs when the “Pandemic Estimator” is greater
than the “Pandemic Threshold”. Finally we use the results for influenza. We
see that the model can predict probably forthcoming waves of the pandemic
and their strength which are depended on the values of the “Pandemic
Threshold” and the “Pandemic Estimator” parameters.
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2000 Mathematics
Subject Classification. 34C60, 93A30.
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Keywords. SIR
models, infectious disease, pandemic, bifurcation.
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Established
by Vietnam Academy of Science and Technology &
Vietnam Mathematical Society
Published by
Springer since January 2013
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