Abstract:
Tasmanian devils are the largest living carnivorous marsupial found in the wild of Tasmania.
These species are being threatened by a cancerous tumour disease, the Devil Facial Tumour
Disease (DFTD). The disease affects the facial areas and has led to a considerable popula tion decline. In this thesis, mathematical models for transmission of DFTD are developed
and analysed to investigate the significance of feeding and mating related contact, optimal
control and fractional-order change on the long-term dynamics of the disease. The two-sex
models consider two transmission pathways namely, feeding and mating related contact.
The relative transmission rates through mating related contact from male devils to female
devils and vice versa are assumed to be different. Model properties such as positivity and
boundedness were proved to ensure that the models are analysed in a feasible regions of bi ological significance. The model disease thresholds were evaluated and used to analyse the
model properties including existence and stability of steady states. Sensitivity analysis of the
model parameters as input values and the reproduction number as the output values was
carried out using the Latin Hypercube Sampling Scheme. Through sensitivity analysis of
model parameters on the disease threshold, it was observed that feeding related contact rate
has the greatest potential of making the disease epidemic worse when increased. In addition,
the tumour induced death rate and the recovery rate for both male and female devils were
observed to have a high potential of reducing the disease burden increased. Our numerical
results indicated that, higher feeding and mating related contact for both male and female
devils are associated with higher peak values of the infected devils. From optimal control
numerical results, we observed that, the infection is considerably reduced in the presence of
controls. However, the infection is predicted to remain in the population with a smaller num ber of devils affected. More still, in the absence of controls we observed that, the number of
infected devils reaches very high and devastating proportions. It is therefore recommended
that, controls be applied early in the epidemic so as to avert high peaks of the infection. The
modelling work also considered a fractional-order model for the disease transmission dy namics with the presumption that future values of the infection depend on both the current
and previous states, an aspect that constitutes memory of the system. Our results indicated
that increased dependence on previous states predicted lower peaks of infected devils but
higher long-term values in the population. From our results, we recommend that control
measures such as isolation/quarantining be put in place to reduce contact between infected
and healthy devils to reduce the disease burden. In addition culling infected devils and vac cination of the uninfected were predicted to be important in reducing the infection as well
as avoid extinction of the devils population and therefore should be implemented to contain
the disease.
