| |
|
The application of mathematics to epidemiological theory is a rapidly growing field which shows a great
deal of promise, both in terms of pure research and in terms of benefit to policy-makers in determining
the best possible actions for maximizing public health. The researchers at MathEcology are highly
skilled at the development of mathematical models in epidemiology at a variety of levels; below is just
a small sample of the type work we have done in this area.
|
| Schistosomiasis |
| West Nile Virus |
| Chronic Wasting Disease |
| |
|
| |
|
Considered second only to malaria in socioeconomic and public health importance in tropical and
subtropical areas, schistosomiasis is a disease caused by internal parasites picked up through contact
with contaminated water. Globally, the human population has almost universal susceptibility to this
scourge and variable or only poorly defined resistance. Although schistosomiasis is associated with
low mortality (though mortality rates due to the disease are underreported and probably underestimated),
it has high morbidity and can cause severe debilitating illness. The majority of infections, however,
go unnoticed and have asymptomatic courses.
|
 |
|
The geographical distribution of schistosomes depends on the existence of suitable conditions for
their intermediate snail hosts. Thus in large part, discussing the environmental conditions which
affect schistosomiasis transmission means discussing those situations in which the appropriate snail
species can survive and thrive. Factors which have the greatest impact on snail survival include:
slope, elevation, and water depth; temperature, precipitation, and seasons; water quality; aquatic
vegetation; and disturbance and water control schemes.
|
 |
|
A reasonable range of values for each of these factors was derived and discussed for each region within
the geographic range of schistosomiasis, and for each of the major schistosome species affecting humans.
With a nod to the reality that all models are generalizations, incorporation of this information into a GIS
model for the geographic distribution of the risk of schistosmiasis transmission can give policy makers
and public health officials valuable tools in the prediction of the global presence of the disease.
|
 |
| [top] |
| |
|
| |
 |
Through an extensive search of current and historical scientific literature, we compiled a mass of
information describing the epidemiology and transmission of West Nile Virus. Lists of susceptible,
vector, reservoir, and amplifying species were summarized and quantified with respect to infection,
transmission, and fatality rates.
|
|
We discussed the potential of key bird species as bioindicators for the disease, and outlined the
risk factors and modes of transmission for susceptible human hosts. All aspects of the epidemiology
of West Nile Virus and the species involved in the transmission cycle were defined and quantified
from the perspective of developing compartmental models for the disease.
|
 |
|
| [top] |
| |
|
| |
|
Chronic wasting disease (CWD) is a fatal neurodegenerative transmissible spongiform encephalopathy
(TSE) affecting North American populations of mule deer, white-tailed deer, black-tailed deer, and
Rocky Mountain Elk, occurring in both captive and free-ranging herds. For this project we performed an
extensive literature search and summary of the current state of knowledge of chronic wasting disease in
North American cervids.
|
 |
CWD is characterized by progressive loss of body condition and steady weight loss, leading to
emaciation and inevitable death. The course of the disease, as well as the point of infectivity, is
poorly known. Data points to the existence of an incubation period, during which the animal shows no
signs of the clinical disease, which lasts an unknown length of time -- from a few weeks to ten months
to fifteen months in deer and 21 months to three years in elk. This leads to the definition of CWD as
an epizootic with a protracted time scale.
The mode of transmission is also poorly characterized, though epidemiological evidence suggests that
transmission may occur at a level apparently unparalleled in other prion diseases. Maternal
transmission may play a role, however models demonstrate that this alone cannot account for current
levels of infection. It is possible that occurrences of maternal transmission are special cases of
horizontal transmission between affected mothers and their offspring. The most likely mode of
transmission is laterally from individual to individual, either through direct contact with infectious
excretions and secretions, or through indirect contact via environmental contamination.
|
| |
 |
The agent causing CWD enters the host via ingestion and crosses the mucous membranes of the digestive
tract, initiating infection in the lymphoid tissues and eventually invading the central nervous system
and accumulating in the brainstem. PrPres, which is associated with CWD, has been detected in
regional lymph nodes tissues as early as six weeks after experimental oral exposure of mule deer fawns
to CWD-infected inoculation. This early accumulation suggests the possible preclinical diagnosis of
the disease via tonsillar biopsy for live deer, however, because PrPres does not appear to accumulate
in lymphoid tissues to the same degree in elk, this technique may not be applicable for early detection
of CWD for this species.
|
|
Management of the disease currently involves quarantine of infected herds and culling of infected
animals, though the lack of early signs during CWD’s potentially infectious incubation period reduces
the effectiveness of such practices. Existing management programs are based on a number of assumptions:
|
| The transition from exposure
to the CWD agent to onset of the clinical disease can be less than thirty-six months; |
| Affected animals may be
infectious as much as eighteen months prior to death; |
| Environmental contamination
is possible in areas where the disease has been established for long time periods. |
|
The knowledge base for chronic wasting disease is, at best, incomplete. The nature of the agent
causing CWD, though suspected to be a prion, is unknown. The modes of transmission are poorly
characterized, as are the point of infectivity and the course of the disease. When developing a
mathematical model for CWD, care must be taken with the use of simplifying assumptions, particularly
the assumption that an infected individual will not transmit the disease until the onset of clinical
signs. The insight gained from incorporating behavioral effects on the infectivity of diseased
individuals, spatial components, and density-dependent effects into a model may by valuable enough to
offset the corresponding increase in model intractability, particularly with respect to disease spread
and persistence in the environment.
|
| | [top] |
|