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A stochastic population pharmacodynamic model of QAP14 in the treatment of lung metastases of 4T1 breast cancer

Journal of Chinese Pharmaceutical Sciences 2021年第10期30卷 794-805页

作者： Mengyi Han Ling Yong Yuchen Guo Xiaoxue Yan Guoshu Chen Daming Kong Tianyan Zhou Beijing Key Laboratory of Molecular Pharmaceutics and New Drug Delivery System Department of PharmaceuticsSchool of Pharmaceutical SciencesPeking UniversityBeijing 100191China Chemical Basic Laboratory School of Chemistry and Chemical EngineeringGuangzhou UniversityGuangzhou 510006China

Cancer metastasis is a process with multi-step complexity and apparent randomness. In this study, we aimed to establish a stochastic mathematical model to describe the random process of cancer metastasis and predict the drug effect of QAP14 on metastasis in a mouse model. The data of lung metastases on the 22^(nd) day after cancer cell implantation with or without the treatment of QAP14, a new chemical compound, were collected in 4T1 breast cancer BALB/c mice. Based on the exponential growth of the primary tumor and metastatic loci, a joint distribution model of metastasis size and number was developed. Disease progression of metastasis and preclinical efficacy of QAP14 were modeled. Parameters M and m representing maximum and minimum of metastasis volume were 3.24 and 0.0184 mm^(3), respectively. The metastasis growth rate γ and metastasis promotion time ρ were estimated and fixed to be 0.0216 d^(-1) and 7.8 d, respectively. The efficacy of QAP14 acted on metastasis promotion time and metastasis growth rate constant in an exponential term, and the effect parameter Effectρ and Effectγ were 16.6 and 0.327 g/mg, respectively. In the present study, we comprehensively characterized the random process of lung metastasis and efficacy of QAP14 in 4T1 breast cancer mice, which might provide a useful reference for the establishment of a clinical population model of cancer metastasis.

关键词： stochastic population model PD model 4T1 Lung metastasis Breast cancer

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Dynamics of delayed stochastic predator-prey models with feedback controls based on discrete observations

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International Journal of Biomathematics 2017年第3期10卷 195-217页

作者： Dianli Zhao Sanling Yuan College of Science University of Shanghai for Science and Technology Shanghai 200093 P R. China

In this paper, we concern a class of the generalized delayed stochastic predator-prey models with feedback coutrols based on discrete observations. The existence of global positive solution is given first. Then we discuss the deterministic model briefly, and establish the necessary conditions and the sufficient conditions for almost-sure extinction and persistence in mean for the stochastic system, where we show that the feedback controls can change the properties of the population systems significantly. Finally, numerical simulations are introduced to support the main results.

关键词： stochastic population model delays feedback controls extinction persis- tence in mean.

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