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Burden of Disease
compartmental model
Drug Therapy
Endemic Equilibrium
Numerical Simulation
Reproduction Number
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Modelling the Transmission Dynamics and Control of the Novel 2009 Swine Influenza (H1N1) Pandemic
Modelling the Transmission Dynamics and Control of the Novel 2009 Swine Influenza (H1N1) Pandemic,10.1007/s115380109538z,Bulletin of Mathematical B
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Modelling the Transmission Dynamics and Control of the Novel 2009 Swine Influenza (H1N1) Pandemic
(
Citations: 1
)
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O. Sharomi
,
C. N. Podder
,
A. B. Gumel
,
S. M. Mahmud
,
E. Rubinstein
The paper presents a deterministic
compartmental model
for the transmission dynamics of swine influenza (H1N1) pandemic in a population in the presence of an imperfect vaccine and use of
drug therapy
for confirmed cases. Rigorous analysis of the model, which stratifies the infected population in terms of their risk of developing severe illness, reveals that it exhibits a vaccineinduced backward bifurcation when the associated
reproduction number
is less than unity. The epidemiological consequence of this result is that the effective control of H1N1, when the
reproduction number
is less than unity, in the population would then be dependent on the initial sizes of the subpopulations of the model. For the case where the vaccine is perfect, it is shown that having the
reproduction number
less than unity is necessary and sufficient for effective control of H1N1 in the population (in such a case, the associated diseasefree equilibrium is globally asymptotically stable). The model has a unique
endemic equilibrium
when the
reproduction number
exceeds unity. Numerical simulations of the model, using data relevant to the province of Manitoba, Canada, show that it reasonably mimics the observed H1N1 pandemic data for Manitoba during the first (Spring) wave of the pandemic. Further, it is shown that the timely implementation of a mass vaccination program together with the size of the Manitoban population that have preexisting infectionacquired immunity (from the first wave) are crucial to the magnitude of the expected
burden of disease
associated with the second wave of the H1N1 pandemic. With an estimated vaccine efficacy of approximately 80%, it is projected that at least 60% of Manitobans need to be vaccinated in order for the effective control or elimination of the H1N1 pandemic in the province to be feasible. Finally, it is shown that the burden of the second wave of H1N1 is expected to be at least three times that of the first wave, and that the second wave would last until the end of January or early February, 2010.
Journal:
Bulletin of Mathematical Biology  BULL MATH BIOL
, vol. 73, no. 3, pp. 515548, 2011
DOI:
10.1007/s115380109538z
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Citation Context
(1)
...Mathematical models are nowadays one of the most effective tools to compare control measures for both human [
2426
] and animal infectious diseases [2730]...
Aurélie Courcoul
,
et al.
Modelling effectiveness of herd level vaccination against Q fever in d...
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Citations
(1)
Modelling effectiveness of herd level vaccination against Q fever in dairy cattle
Aurélie Courcoul
,
Lenny Hogerwerf
,
Don Klinkenberg
,
Mirjam Nielen
,
Elisabeta Vergu
,
François Beaudeau
Journal:
Veterinary Research  VET RES
, vol. 42, no. 1, pp. 19, 2011