Adjoint Sensitivity Analysis of a Spatial Tumor Growth Model with Strong Allee Effect
AbstractThe Allee effect is commonly used in populations models. It is said that certain population model contains Allee effect if it has a specific form of growth function. If the growth function is negative for a low population density (the model has a growth threshold whose below the population goes to extinction) then the effect is called a strong Allee effect. In case when the value of growth function is small for low population density but remains positive it is called a weak Allee effect. The Allee effects in both forms (weak and strong) is used in many models including spatial models of predator-prey interactions. Recent works suggest that the strong Allee effect can be important in the spreading of malignant tumours.
In this work we use the adjoint sensitivity analysis to calculate the so-called spatiotemporal gradient of predefined objective function with respect to irradiation signal in spatial model of tumor growth with introduced the strong Alle effect in the growth function. The calculated gradient can be used to more precisely predict the tumour behaviour and can be also important in developing a more patient-friendly radiotherapy protocols.
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