TY  - Type of reference 
TI  - Analysis of a tumor growth model with treatments 
AU  - Slah Eddin Ben Abdeljalil
 
AU  - Atef Ben Essid
 
AU  - Saloua Mani Aouadi 
AB  - In this paper, we conduct a mathematical analysis of a tumor growth model with treatments. The model consists of a system that describes the evolution of metastatic tumors and the number of cells present in the primary tumor. The former evolution is described by a transport equation, and the latter by an ordinary differential equation of Gompertzian type. The two dynamics are coupled through a nonlocal boundary condition that takes into account the tumor colonization rate. We prove an existence result where the main difficulty is to handle the coupling and to take into account the time discontinuities generated by treatment terms. The proof is based on a Banach fixed point theorem in a suitable functional space. We also develop a computational code based on the method of characteristics and present numerical tests that highlight the effects of different therapies. 
DO  - 10.21494/ISTE.OP.2024.1099 
JF  - Advances in Pure and Applied Mathematics 
KW  - Ordinary differential equations, Partial differential equations, Discontinuous data, Tumor growth, Ordinary differential equations, Partial differential equations, Discontinuous data, Tumor growth,  
L1  - http://www.openscience.fr/IMG/pdf/iste_apam24v15n2_2.pdf 
LA  - en 
PB  - ISTE OpenScience 
DA  - 2024/03/7 
SN  - 1869-6090 
TT  - Analyse d’un modèle de croissance d’une tumeur avec traitements  
UR  - http://www.openscience.fr/Analysis-of-a-tumor-growth-model-with-treatments 
IS  - Issue 2 (Special CSMT 2023) 
VL  - 15 
ER  -