RESUMO
We develop and analyze a mathematical model of oncolytic virotherapy in the treatment of melanoma. We begin with a special, local case of the model, in which we consider the dynamics of the tumour cells in the presence of an oncolytic virus at the primary tumour site. We then consider the more general regional model, in which we incorporate a linear network of lymph nodes through which the tumour cells and the oncolytic virus may spread. The modelling also considers the impact of hypoxia on the disease dynamics. The modelling takes into account both the effects of hypoxia on tumour growth and spreading, as well as the impact of hypoxia on oncolytic virotherapy as a treatment modality. We find that oxygen-rich environments are favourable for the use of adenoviruses as oncolytic agents, potentially suggesting the use of complementary external oxygenation as a key aspect of treatment. Furthermore, the delicate balance between a virus' infection capabilities and its oncolytic capabilities should be considered when engineering an oncolytic virus. If the virus is too potent at killing tumour cells while not being sufficiently effective at infecting them, the infected tumour cells are destroyed faster than they are able to infect additional tumour cells, leading less favourable clinical results. Numerical simulations are performed in order to support the analytic results and to further investigate the impact of various parameters on the outcomes of treatment. Our modelling provides further evidence indicating the importance of three key factors in treatment outcomes: tumour microenvironment oxygen concentration, viral infection rates, and viral oncolysis rates. The numerical results also provide some estimates on these key model parameters which may be useful in the engineering of oncolytic adenoviruses.
RESUMO
The continual distress of COVID-19 cannot be overemphasized. The pandemic economic and social costs are alarming, with recent attributed economic loss amounting to billions of dollars globally. This economic loss is partly driven by workplace absenteeism due to the disease. Influenza is believed to be a culprit in reinforcing this phenomenon as it may exist in the population concurrently with COVID-19 during the influenza season. Furthermore, their joint infection may increase workplace absenteeism leading to additional economic loss. The objective of this project will aim to quantify the collective impact of COVID-19 and influenza on workplace absenteeism via a mathematical compartmental disease model incorporating population screening and vaccination. Our results indicate that appropriate PCR testing and vaccination of both COVID-19 and seasonal influenza may significantly alleviate workplace absenteeism. However, with COVID-19 PCR testing, there may be a critical threshold where additional tests may result in diminishing returns. Regardless, we recommend on-going PCR testing as a public health intervention accompanying concurrent COVID-19 and influenza vaccination with the added caveat that sensitivity analyses will be necessary to determine the optimal thresholds for both testing and vaccine coverage. Overall, our results suggest that rates of COVID-19 vaccination and PCR testing capacity are important factors for reducing absenteeism, while the influenza vaccination rate and the transmission rates for both COVID-19 and influenza have lower and almost equal affect on absenteeism. We also use the model to estimate and quantify the (indirect) benefit that influenza immunization confers against COVID-19 transmission.
RESUMO
We explore the dynamics of invasive weeds by partial differential equation (PDE) modelling and applying dynamical system and phase portrait techniques. We begin by applying the method of characteristics to a preexisting PDE model of the spreading of T. fluminensis, an invasive weed which has been responsible for native forest depletion. We explore the system both at particular points in space and over all of space, in one dimension, as a function of time. Our model suggests that an increase in the rate of spread of the weed through space will increase the efficacy of control measures taken at the weed's spatial boundary. We then propose new competition models based on the previous model and explore the existence of travelling wave solutions. These models represent both the cases with (i) a competing native plant species which spreads through the forest and (ii) a non-mobile, established native plant species. In the former case, the model suggests that an increased mass-action coefficient between the competing species is sufficient and necessary for the transition of the forest into a state of coexistence. In the latter case, the result is not as strong: a sufficiently large rate of competition between the species excludes the possibility of native plant extinction and hence suggests that forest depletion will not occur, but does not imply coexistence. We perform some numerical simulations to support our analytic results. In all cases, we give a discussion on the physical and biological interpretations of our results. We conclude with some suggestions for future work and with a discussion of the advantages and disadvantages of the methods.
