The growth dynamics of tumor subject to both immune surveillance and external therapy intervention

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Considering the growth of tumor cells modeled by an enzyme dynamic process under an immune surveillance, we studied in anti-tumor immunotherapy the single-variable growth dynamics of tumor cells subject to a multiplicative noise and an external therapy intervention simultaneously. The law of tumor growth of the above anti-tumor immunotherapy model was revealed through numerical simula- tions to the relevant stochastic dynamic differential equation. Two simulative parameters of therapy, i.e., therapy intensity and therapy duty-cycle, were introduced to characterize a treatment process similar to a tumor clinic therapy. There exists a critical therapy boundary which, in an expo- nent-decaying form, divides the parameter region of therapy into an invalid and a valid treatment zone, respectively. A greater critical therapy duty-cycle is necessary to achieve a valid treatment for a lower therapy intensity while the critical therapy intensity decreases accordingly with an enhancing immunity. A primary clinic observation of the patients with the typical non-hodgekin’s lymphoma was carried out, and there appears a basic agreement between clinic observations and dynamic simulations. Considering the growth of tumor cells modeled by an enzyme dynamic process under an immune surveillance, we studied in anti-tumor immunotherapy the single-variable growth dynamics of tumor cells subject to a multiplicative noise and an external therapy intervention. The law of tumor growth of the above anti-tumor immunotherapy model was revealed through numerical simulati- tions to the relevant stochastic dynamic differential equation. Two simulative parameters of therapy, ie, therapy intensity and therapy duty-cycle, were introduced to characterize a treatment process similar to a tumor there is a critical therapy boundary which, in an expo- nent-decaying form, divides the parameter region of therapy into an invalid and a valid treatment zone, respectively. A greater critical therapy duty-cycle is necessary to achieve a valid treatment for a lower therapy intensity while the critical therapy intensity decreased accordingly with an enhancing immunity. A primary clinic observation of the patients with the typical non-hodgekin’s lymphoma was carried out, and there appears a basic agreement between clinic observations and dynamic simulations.
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