Browsing by Author "Winnie Wanja, Chabaari"

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    Intracellular and immune-response delays effects on the interation between tumor cells, oncolytic viruses and the immune system
    (Stellenbosch : Stellenbosch University, 2019-12) Winnie Wanja, Chabaari; Pulliam, Juliet R. C.; Ouifki, Rachid; Eladdadi, Amina; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences
    ENGLISH ABSTRACT: Lately, oncolytic viruses have been used to mitigate cancer as they lyse tumor cells whilst leaving normal cells largely unharmed (as opposed to many other forms of cancer treatment). The oncolytic effect depends on both viral replication ability and immune response type induced by said replication. A major challenge posed by this therapy is any potential delay that can occur during viral replication, combined with a fast immune response. For this project, we will investigate possible trade-offs of the interactions, with particular focus on the effect(s) of delay.We will extend recently published mathematical models on virotherapy by taking into account the simultaneous effect of the delay and considering various forms of virus-cell infections. We perform stability analysis with the delay and run numerical simulations to confirm the mathematical findings and see how well this model would fit data or whether by the introduction of the delay terms, we improve the fit of the data. Eventually, we derive an explicit formula for the trade-off between the two delays that leads to tumor eradication. One of the main findings is the occurrence of a delay-induced Hopf bifurcation, indicative of tumor relapse which is a confirmation of other previous cancer virotherapy mathematical models.