Mass action rate law for irreversible reactions

Reaction scheme where the products are created from the reactants and the change of a product quantity is proportional to the product of reactant activities. The reaction scheme does not include any reverse process that creates the reactants from the products. The change of a product quantity is proportional to the quantity of one reactant.

k1*PRODUCT<substrate_i> 2019-07-26T13:28:15Z r*P*(1-k*P) 2019-07-26T13:29:19Z d*I*T/(y+T) 2019-07-26T13:30:10Z v*S*M 2019-07-26T13:30:57Z T*I*v 2019-07-26T13:33:15Z R*(s1*T*(1-s2*T))/(3*(1-(T+Td))) 2019-07-26T13:33:15Z R*u2*Td/(3*(1-(T+Td))) 2019-07-26T11:13:26Z jm2187@cam.ac.uk Men Jinghao University of Cambridge The paper describes a model of immune-cancer interaction. One time unit=24 days. Created by COPASI 4.25 (Build 207) This model is described in the article: Mathematical analysis of a tumour-immune interaction model: A moving boundary problem Joseph Malinzi and Innocenter Amima Mathematical Biosciences 308 (2019) 8–19 Abstract: IA spatio-temporal mathematical model, in the form of a moving boundary problem, to explain cancer dormancy is developed. Analysis of the model is carried out for both temporal and spatio-temporal cases. Stability analysis and numerical simulations of the temporal model replicate experimental observations of immune-induced tu- mour dormancy. Travelling wave solutions of the spatio-temporal model are determined using the hyperbolic tangent method and minimum wave speeds of invasion are calculated. Travelling wave analysis depicts that cell invasion dynamics are mainly driven by their motion and growth rates. A stability analysis of the spatio-tem- poral model shows a possibility of dynamical stabilization of the tumour-free steady state. Simulation results reveal that the tumour swells to a dormant level. To cite BioModels Database, please use: BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models . To the extent possible under law, all copyright and related or neighbouring rights to this encoded model have been dedicated to the public domain worldwide. Please refer to CC0 Public Domain Dedication for more information. 2019-07-26T13:18:00Z 2019-07-26T13:18:22Z immune cells density unit /1e6 cells cm-3 2019-07-26T13:18:26Z tumor cells density unit /1e6 cells cm-3 2019-07-26T13:18:28Z dead tumor cells density unit /1e6 cells cm-3 2019-07-26T13:18:30Z chemokine concentration 2019-07-26T13:18:33Z tumor radius/cm 2019-07-26T13:23:21Z 1 2019-07-26T13:23:22Z 1 2019-07-26T13:23:26Z 1 2019-07-26T13:23:27Z 1 2019-07-26T13:23:29Z 1 2019-07-26T13:23:31Z 1 2019-07-26T13:23:32Z 1 2019-07-26T13:23:34Z 1 2019-07-26T13:23:35Z 1 2019-07-26T13:23:38Z 1 2019-07-26T13:23:41Z 1 2019-07-26T13:32:46Z michaelis menten constant 1 2019-07-26T13:25:20Z 2019-07-26T13:25:25Z 2019-07-26T13:25:29Z 2019-07-26T13:25:33Z 2019-07-26T13:25:36Z 2019-07-26T13:25:51Z 2019-07-26T13:25:55Z 2019-07-26T13:26:04Z 2019-07-26T13:26:08Z 2019-07-26T13:26:14Z 2019-07-26T13:26:17Z 2019-07-26T14:09:57Z <CN=Root,Model=Malinzi2018 - tumor-immune interaction,Vector=Values[f1],Reference=InitialValue> <CN=Root,Model=Malinzi2018 - tumor-immune interaction,Vector=Values[f2],Reference=InitialValue> <CN=Root,Model=Malinzi2018 - tumor-immune interaction,Vector=Values[y],Reference=InitialValue> <CN=Root,Model=Malinzi2018 - tumor-immune interaction,Vector=Values[d],Reference=InitialValue> <CN=Root,Model=Malinzi2018 - tumor-immune interaction,Vector=Values[v1],Reference=InitialValue> <CN=Root,Model=Malinzi2018 - tumor-immune interaction,Vector=Values[s1],Reference=InitialValue> <CN=Root,Model=Malinzi2018 - tumor-immune interaction,Vector=Values[s2],Reference=InitialValue> <CN=Root,Model=Malinzi2018 - tumor-immune interaction,Vector=Values[v2],Reference=InitialValue> <CN=Root,Model=Malinzi2018 - tumor-immune interaction,Vector=Values[v3],Reference=InitialValue> <CN=Root,Model=Malinzi2018 - tumor-immune interaction,Vector=Values[u1],Reference=InitialValue> <CN=Root,Model=Malinzi2018 - tumor-immune interaction,Vector=Values[r],Reference=InitialValue> <CN=Root,Model=Malinzi2018 - tumor-immune interaction,Vector=Values[u2],Reference=InitialValue> <CN=Root,Model=Malinzi2018 - tumor-immune interaction,Vector=Values[s1],Reference=InitialValue> <CN=Root,Model=Malinzi2018 - tumor-immune interaction,Vector=Values[s2],Reference=InitialValue> <CN=Root,Model=Malinzi2018 - tumor-immune interaction,Vector=Values[u2],Reference=InitialValue> 0 0.29999999999999999 0.80000000000000004 0.10000000000000001 9.9999999999999995e-07 0.80000000000000004 1 1.3398000000000001 0.25 3.0217999999999998 0.0021800000000000001 3.8835000000000002 0.5 0.72789999999999999 300 1 0.10000000000000001 0.23999999999999999 202 Automatically generated report.