Narrow Results

NEWS – Lilly and Innovent Biologics enter strategic alliance; one of the largest biotech drug development collaborations in China.

NEWS – ZAI Lab enrolls first patient in Phase 1 study of ZL-2102.

NEWS – LamdaGen Corporation launches Taiwan diagnostic subsidiary.

NEWS – 3M makes a greater commitment in China's West Region; Plans for a new customer technical center.

NEWS – NCKU launches campus food ingredients registration platform.

NEWS – Lab-free immune therapy developed.

NEWS – Hainan Province, Hengda Health and Korean Yuanchen enter strategic cooperation agreement.

NEWS – Bristol-Myers Squibb and ZAI Lab enter licensing agreement to develop, manufacture and commercialize brivanib in China.

NEWS – Concord Medical acquires Fortis Surgical Hospital in Singapore.

NEWS – Merck Animal Health and China Animal Husbandry Industry Co., Ltd establish partnership.

NEWS – Helsinn Group signs exclusive agreement with Mundipharma for distribution and license of anamorelin in China, Hong Kong and Macau.

NEWS – C-FDA approves IND for D-Pharm's anti-epileptic drug, DP-VPA in China.

NEWS – Waters' UPLC I-Class/Xevo TQ-S System approved for in vitro diagnostic use in China.

NEWS – Vitruvias Therapeutics and Sunny Pharmtech form partnership to co-develop several high value generic drugs.

NEWS – Professor Xie Xiaoliang first Chinese Albany Award winner.

RESEARCH INSTITUTES – A look at Duke Kunshan University Global Health Research Center.

RESEARCH INSTITUTES – The NYU-ECNU Institute of Brain and Cognitive Science.

In this paper, I continue the study of the mathematical models presented in [J. C. Larsen, Models of cancer growth, J. Appl. Math. Comput.53(1–2) (2015) 613–645] and [J. C. Larsen, The bistability theorem in a model of metastatic cancer, to appear in Appl. Math.]. I shall prove the bistability theorem for the ODE model from [Larsen, 2015]. It is a mass action kinetic system in the variables $C$ cancer, GF growth factor and GI growth inhibitor. This theorem says that for some values of the parameters, there exist two positive singular points $c_{\ast }^{+}=(C_{\ast }^{+},{\mathrm{\text{GF}}}_{\ast },{\mathrm{\text{GI}}}_{\ast }^{+})$, $c_{\ast }^{-}=(C_{\ast }^{-},{\mathrm{\text{GF}}}_{\ast },{\mathrm{\text{GI}}}_{\ast }^{-})$ of the vector field. Here $C_{\ast }^{-}<C_{\ast }^{+}$ and $c_{\ast }^{-}$ is stable and $c_{\ast }^{+}$ is unstable, see Sec. 2. There is also a discrete model in [Larsen, 2015], it is a linear map ($T$) on three-dimensional Euclidean vector space with variables $(C,\mathrm{\text{GF}},\mathrm{\text{GI}}),$ where these variables have the same meaning as in the ODE model above. In [Larsen, 2015], I showed that one can sometimes find affine vector fields on three-dimensional Euclidean vector space whose time one map is $T$. I shall also show this in the present paper in a more general setting than in [Larsen, 2015]. This enables me to find an expression for the rate of change of cancer growth on the coordinate hyperplane $C=0$ in Euclidean vector space. I also present an ODE model of cancer metastasis with variables $C,C_M,\mathrm{\text{GF}},\mathrm{\text{GI}},$ where $C$ is primary cancer and $C_M$ is metastatic cancer and GF, GI are growth factors and growth inhibitors, respectively.