arXiv subjects

Meir Shillor

Publications and source records attributed to Meir Shillor.

4 recordsLinked to original sources

arXiv2026

A Mathematical Model for Chemotherapy, Immunotherapy and Virotherapy Treatments of Cancer

We continue our study of a model for cancer treatment, constructed in Dutta et. al., 2025, by adding Virotherapy to the Chemotherapy and Immunotherapy studied there. It is a dynamical system model for the spread of cancer in healthy tissue. It allows computer experiments of various combinations of the three modalities, which cannot be performed in the laboratory or experimentally. The novelty is the addition of Virotherapy. The analysis shows that the model solutions exist, are bounded, and nonnegative on each finite time interval, thus biologically feasible. A time-stepping algorithm is constructed and implemented, and computer simulations are presented. The simulations show the development of the disease under various treatment options, including a baseline case without treatment, cases for each of the three treatments separately, and some combinations of the three treatments. These simulations indicate that combinations of treatments are more effective. However, we do not consider any limitation or incompatibilities of the joint application of the three modalities, that may exist in practice. Once validated in the field, the model can be used to design treatment schedules of combinations of the three modalities for improved outcomes.

q-bio.OT↗

arXiv2021

A mathematical model of the COVID-19 pandemic dynamics with dependent variable infection rate: Application to the Republic of Korea

This work constructs, analyzes, and simulates a new compartmental SEIR-type model for the dynamics and potential control of the current COVID-19 pandemic. The novelty in this work is two-fold. First, the population is divided according to its compliance with disease control directives (lockdown, shelter-in-place, masks/face coverings, physical distancing, etc.) into those who fully comply and those who follow the directives partially, or are necessarily mobile (such as medical staff). This split, indirectly, reflects on the quality and consistency of these measures. This allows the assessment of the overall effectiveness of the control measures and the impact of their relaxing or tightening on the disease spread. Second, the adequate contact rate, which directly affects the infection rate, is one of the model unknowns, as it keeps track of the changes in the population behavior and the effectiveness of various disease treatment modalities via a differential inclusion. Existence, uniqueness and positivity results are proved using a nonstandard convex analysis-based approach. As a case study, the pandemic outbreak in the Republic of Korea (South Korea) is simulated. The model parameters were found by minimizing the deviation of the model prediction from the reported data over the first 100 days of the pandemic in South Korea.The simulations show that the model captures accurately the pandemic dynamics in the subsequent 75 days, which provides confidence in the model predictions and its future use. In particular, the model predicts that about 40% of the infections were not documented, which implies that asymptomatic infections contribute silently but substantially to the spread of the disease indicating that more widespread asymptomatic testing is necessary.

q-bio.PE↗

arXiv2019

A frictional contact problem with wear diffusion

This paper constructs and analyzes a model for the dynamic frictional contact between a viscoelastic body and a moving foundation. The contact involves wear of the contacting surface and the diffusion of the wear debris. The relationships between the stresses and displacements on the contact boundary are modeled by the normal compliance law and a version of the Coulomb law of dry friction. The rate of wear of the contact surface is described by the differential form of the Archard law. The effects of the diffusion of the wear particles that cannot leave the contact surface on the surface are taken into account. The novelty of this work is that the contact surface is a manifold and, consequently, the diffusion of the debris takes place on a curved surface. The interest in the model is related to the wear of mechanical joints and orthopedic biomechanics where the wear debris are trapped, they diffuse and often cause the degradation of the properties of joint prosthesis and various implants. The model is in the form of a differential inclusion for the mechanical contact and the diffusion equation for the wear debris on the contacting surface. The existence of a weak solution is proved by using a truncation argument and the Kakutani--Ky Fan--Glicksberg fixed point theorem.

math-ph↗

arXiv2019

Dynamic thermoviscoelastic thermistor problem with contact and nonmonotone friction

The paper studies the evolution of the thermomechanical and electric state of a thermoviscoelastic thermistor that is in frictional contact with a reactive foundation. The mechanical process is dynamic, while the electric process is quasistatic. Friction is modeled with a nonmonotone relation between the tangential traction and tangential velocity. Frictional heat generation is taken into account and so is the strong dependence of the electric conductivity on the temperature. The mathematical model for the process is in the form of a system that consists of dynamic hyperbolic subdifferential inclusion for the mechanical state coupled with a nonlinear parabolic equation for the temperature and an elliptic equation for the electric potential. The paper establishes the existence of a weak solution to the problem by using time delays, a priori estimates and a convergence method.

math-ph↗