Modeling seasonal behavior changes and disease transmission with application to chronic wasting disease
Modeling seasonal behavior changes and disease transmission with
application to chronic wasting disease
Tamer Orabya, Corresponding author contact information E-mail the
corresponding author, Olga Vasilyevab, Daniel Krewskia, c, Frithjof Lutscherb a
McLaughlin Centre for Population Health Risk Assessment, University of Ottawa,
Ottawa, Ontario, Canada b Department of Mathematics and Statistics, University
of Ottawa, Ottawa, Ontario, Canada c Department of Epidemiology and Community
Medicine, Faculty of Medicine, University of Ottawa, Ottawa, Ontario, Canada
Highlights
• A new model is built to study spread chronic wasting disease in
free-ranging deer.
• The model employs two modes of transmission based on seasonal
behavior.
• Birth and change in seasonal home range are impulsive.
• The basic reproduction number and stability of disease-free equilibrium
are studied.
• Under certain conditions, culling can eradicate the disease.
Behavior and habitat of wildlife animals change seasonally according to
environmental conditions. Mathematical models need to represent this seasonality
to be able to make realistic predictions about the future of a population and
the effectiveness of human interventions. Managing and modeling disease in wild
animal populations requires particular care in that disease transmission
dynamics is a critical consideration in the etiology of both human and animal
diseases, with different transmission paradigms requiring different disease risk
management strategies. Since transmission of infectious diseases among wildlife
depends strongly on social behavior, mechanisms of disease transmission could
also change seasonally. A specific consideration in this regard confronted by
modellers is whether the contact rate between individuals is density-dependent
or frequency-dependent. We argue that seasonal behavior changes could lead to a
seasonal shift between density and frequency dependence. This hypothesis is
explored in the case of chronic wasting disease (CWD), a fatal disease that
affects deer, elk and moose in many areas of North America. Specifically, we
introduce a strategic CWD risk model based on direct disease transmission that
accounts for the seasonal change in the transmission dynamics and habitats
occupied, guided by information derived from cervid ecology. The model is
composed of summer and winter susceptible-infected (SI) equations, with
frequency-dependent and density-dependent transmission dynamics, respectively.
The model includes impulsive birth events with density-dependent birth rate. We
determine the basic reproduction number as a weighted average of two seasonal
reproduction numbers. We parameterize the model from data derived from the
scientific literature on CWD and deer ecology, and conduct global and local
sensitivity analyses of the basic reproduction number. We explore the
effectiveness of different culling strategies for the management of CWD:
although summer culling seems to be an effective disease eradication strategy,
the total culling rate is limited by the requirement to preserve the herd.
snip...
4. Discussion
Most modeling studies of human and wildlife disease assume that the
mechanism of individual contacts and therefore the functional dependence of the
force of infection remains unchanged, even if parameters may vary seasonally.
Instead, we argue that seasonal changes in behavior can lead to a more
fundamental change in the disease transmission mechanism (see also Potapov et
al., 2013), so that the functional dependence of the force of infection changes
seasonally. In particular, roaming and aggregation behavior in wildlife
populations could lead to a shift from DD to FD disease transmission. We
developed and analyzed a simple, strategic model for such a shift, and applied
it to CWD in deer. In principle, these same considerations could be applied to
modeling of childhood diseases that show outbreak patterns highly correlated
with school terms. Such an approach could give a more mechanistic underpinning
of the contact rate, which is often formulated as a periodically forced
function. An interesting future topic is to compare the predictions of a
multi-season model to those of a temporally constant model where disease
transmission is modeled by some suitably interpolated transmission term.
The simplicity of our model allows for an elegant reduction to a pair of
impulsive equations and an explicit expression for R0. While culling is a viable
control strategy in pure DD models, it is not in pure FD models (Lloyd-Smith et
al., 2005). We found that culling can be a useful control strategy in our
two-season model, but culling rates need to be chosen carefully to ensure
survival of the herd(see also Choisy and Rohani, 2006). According to our
analysis, the contact rate during the summer season has greater influence on R0
than the contact rate during the winter. Previous authors had argued otherwise
(Habib et al., 2011). Accordingly, if culling were equally costly during the
summer and winter, we argue that harvesting efforts should be concentrated in
the summer.However, since herds tend to be spread out over larger areas during
the summer, this might not be feasible. Our analysis also shows that increasing
the length of the summer season, as predicted under some global change
scenarios, would increase R0 and make disease eradication more difficult.
There is a long-standing discussion about whether DD or FD is a more
appropriate modeling assumption in a given situation (Begon et al., 2002;
Lloyd-Smith et al., 2005). For wildlife diseases, FD is sometimes favored
(McCallum et al., 2001; Begon et al., 1999), but deciding between the two
alternatives based on data fitting is often difficult, and, in the case of CWD,
remains unclear (Wasserbergetal.,2009). We speculate that some of the confusion
may arise by pooling data from different seasons when different transmission
mechanisms may be operating. In practice, transmission may be neither ‘purely’
DD nor ‘purely’ FD. Some authors have addressed this problem by employing
various interpolations between DD and FD (Almberg et al., 2011; Habib et al.,
2011). In practice, model selection criteria are then required to decide whether
the improved fit to data warrants the inclusion of an additional parameter. Our
modeling approach also works for such interpolated forms of disease
transmission; however, an explicit solution necessary for model reduction is not
available. The relative size of the habitat that the herd occupies in different
seasons would then affect R0 and all other model characteristics.
We are currently extending this work to include the rut season explicitly,
where social behavior changes again, so that disease transmission might change,
and where harvesting is not allowed. At that point, gender and potentially age
structure should also be introduced into the population since males, females and
fawns engage in social contact in very different ways; see Al-arydah et al.
(2012) for an age and gender-structured model of CWD. Such a model is too
complex to yield explicit solutions, so that the analysis has to proceed
numerically. Our results here can inspire simulation studies of the properties
of such a model, and our weighted average formula for R0 can provide guidance
for R0 in a more complex model.
So far,we considered only one of the three potential transmission pathways,
namely direct transmission. The extension of our model to include vertical
transmission is straight forward, and all the analytical results can be extended
(see Appendix D). The basic reproduction number increases as the probability of
vertical transmission increases. Since there are no reliable estimates of the
vertical transmission probability, we did not include it in our sensitivity
analysis.
The inclusion of environmental transmission into our model is a lot more
delicate and is beyond the scope of this work. A number of recent empirical and
theoretical studies point to the importance of environmental transmission of CWD
in addition to, or instead of, direct contact transmission (Almberg et al.,
2011; Miller et al., 2004; Wasserberg et al., 2009; Smith et al., 2011; Johnson
et al., 2006). To justify the absence of an environmental compartment in many
models, it is typically argued that since the rate of degradation of the
environmentally available CWD agent is faster than the prevalence growth rate,
this compartment will be proportional to the number of infected individuals and
hence can be incorporated into direct transmission (Potapovetal., 2012). A more
thorough investigation into the conditions under which indirect transmission can
be modeled as direct transmission was recently given by Breban (2013).
Environmental transmission is relatively easily explicitly incorporated
into the disease model when the herd remains in the same location. One needs to
add an ‘environmental’ compartment and define appropriate deposition and uptake
functions for the CWD agent (prions) (Almberg et al., 2011; Vasilyeva et al.,
submitted for publication). Model formulation is more challenging when a herd
migrates between seasons. Since environmental prions are not expected to decay
within a single season, one needs to keep track of prions in the winter and
summer areas separately, there by introducing an additional compartment to the
model. If summer and winter areas overlap, the modeling process becomes even
more difficult. It is also unclear to what degree environmental prions are
available for uptake under snow cover. Based on our results without
environmental transmission, we speculate that if the herd is much more
aggregated during the winter, then the prion concentration is much higher in the
winter season, and that R0 would be more sensitive to (some) winter parameters
than summer parameters.
We believe that by splitting the year into different seasons where
different behavioral mechanisms such as aggregation and reproduction operate,
our model can capture important aspects of disease etiology not embodied in
current models, thereby facilitating investigation of questions related to
optimal timing of disease control,as well as other issues that have a seasonal
dimension.
Friday, November 29, 2013
Identification of Misfolded Proteins in Body Fluids for the Diagnosis of
Prion Diseases
International Journal of Cell Biology
Friday, November 22, 2013
*** Wasting disease is threat to the entire UK deer population CWD TSE
PRION DISEASE Singeltary submission to Scottish Parliament
Sunday, December 29, 2013
Impacts of wildlife baiting and supplemental feeding on infectious disease
transmission risk: A synthesis of knowledge
Sunday, November 3, 2013
*** Environmental Impact Statements; Availability, etc.: Animal Carcass
Management [Docket No. APHIS-2013-0044]
Wednesday, September 04, 2013
***cwd - cervid captive livestock escapes, loose and on the run in the
wild...
Saturday, February 04, 2012
Wisconsin 16 MONTH age limit on testing dead deer Game Farm CWD Testing
Protocol Needs To Be Revised
PRION2013 CONGRESSIONAL ABSTRACTS CWD
Thursday, August 08, 2013
Characterization of the first case of naturally occurring chronic wasting
disease in a captive red deer (Cervus elaphus) in North America
Friday, August 09, 2013
***CWD TSE prion, plants, vegetables, and the potential for environmental
contamination
Sunday, September 01, 2013
hunting over gut piles and CWD TSE prion disease
Monday, October 07, 2013
The importance of localized culling in stabilizing chronic wasting disease
prevalence in white-tailed deer populations
Friday, December 14, 2012
DEFRA U.K. What is the risk of Chronic Wasting Disease CWD being introduced
into Great Britain? A Qualitative Risk Assessment October 2012
Saturday, March 10, 2012
CWD, GAME FARMS, urine, feces, soil, lichens, and banned mad cow protein
feed CUSTOM MADE for deer and elk
PRION2013 CONGRESSIONAL ABSTRACTS CWD
Sunday, August 25, 2013
***Chronic Wasting Disease CWD risk factors, *humans*, domestic cats,
blood, and mother to offspring transmission
Sunday, July 21, 2013
*** As Chronic Wasting Disease CWD rises in deer herd, what about risk for
humans?
Saturday, December 21, 2013
Parelaphostrongylus (Brainworm) Infection in Deer and Elk and the potential
for CWD TSE prion consumption and spreading there from ?
Sunday, December 15, 2013
*** FDA PART 589 -- SUBSTANCES PROHIBITED FROM USE IN ANIMAL FOOD OR FEED
VIOLATIONS OFFICIAL ACTION INDICATED OIA UPDATE DECEMBER 2013 UPDATE ***
Saturday, December 21, 2013
**** Complementary studies detecting classical bovine spongiform
encephalopathy infectivity in jejunum, ileum and ileocaecal junction in
incubating cattle ****
TSS
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