Modelling the significance of feeding and mating related contact, optimal control and fractional order change on the long term dynamics of Devil Facial Tumour Disease

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.