Avian influenza is a contagious viral disease caused by influenza
virus type A. Avian influenza can be disastrous (if it occurs), due to
the short incubation period (about 1--4 days). Thus it is important to
study this disease so that we are more prepared to manage it in the
future. A classical system of differential equations (the
half-saturated incidence model) and three Filippov models --- an
avian-only model with culling of infected birds, an SIIR
(Susceptible-Infected-Infected-Recovered) model with quarantine of
infected humans and an avian-only model with culling both susceptible
and infected birds --- that are governed by ordinary differential
equations with discontinuous right-hand sides (i.e., differential
inclusion) are proposed to study the transmission of avian
influenza. The effect of half-saturated incidence is investigated, and
the outcome of this model is compared with the bilinear incidence
model. Both models remain endemic whenever their respective basic
reproduction numbers are greater than one. The
half-saturated incidence model generates more infected individuals
than the bilinear incidence model. This may be because the
bilinear incidence model is underestimating the number of infected
individuals at the outbreak. For the Filippov models,
the number of infected individuals is used as a reference in applying
control strategies. If this number is greater than a threshold value,
a control measure has to be employed immediately to avoid a more
severe outbreak. Otherwise, no action is necessary. We perform
dynamical system analysis for all models. The existence of sliding
modes and the flow on the discontinuity surfaces are determined. In
addition, numerical simulations are conducted to illustrate the
dynamics of the models. Our results suggest that if appropriate
tolerance thresholds are chosen such that all trajectories of the
Filippov models are converging to an equilibrium point that lies in
the region below the infected tolerance threshold or on the
discontinuity surface, then no control strategy is necessary as we
consider the outbreak is tolerable. Otherwise, we have to apply
control strategies to contain the outbreak. Hence a well-defined
threshold policy is crucial for us to combat avian influenza
effectively.
| Identifer | oai:union.ndltd.org:uottawa.ca/oai:ruor.uottawa.ca:10393/35818 |
| Date | January 2017 |
| Creators | Chong, Nyuk Sian |
| Contributors | Smith, Robert, Dionne, Benoit |
| Publisher | Université d'Ottawa / University of Ottawa |
| Source Sets | Université d’Ottawa |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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