Frank Nani

A mathematical model of cancer treatment by immunotherapy

In this paper, a detailed mathematical study of cancer immunotherapy will be presented. General principles of cancer immunotherapy and the model equations and hypotheses will be discussed. Mathematical analyses of the model equations with regard to dissipativity, boundedness of solutions, invariance of non-negativity, nature of equilibria, persistence, extinction and global stability will be analyzed. It will also be shown that bifurcations can occur, and criteria for total cure will also be derived.

A chemotherapy model for the treatment of cancer with metastasis

In this paper, we propose and analyse a mathematical model of cancer treatment by chemotherapy where there is metastasis from a primary to a secondary site by the cancer cells. We view the interactions between normal and cancer cells as being competitive for available resources, and we think of the chemotherapy agent as a predator on both normal and cancer cells. The metastasis may be time delayed. The analysis is carried out both analytically (where possible) and numerically. In particular, we look at the existence and stability of equilibria of our model, which consists of six differential equations. As well, we investigate (numerically) the behavior of solutions for various values of the parameters.

Computer simulation of a mathematical model of HAART therapy for HIV-1 AIDS

A clinically plausible mathematical model is constructed to describe the patho-physiological dynamics of HIV-1 induced AIDS during HAART therapy. The model equations incorporate physiological interactions between non-infected helper T cells, HIV-1 infected helper T cells, HIV-1 virions in the blood plasma, HIV-1 specific cytotoxic T cells and drug molecules of the HAART protocol. Investigative computer simulations are performed to elucidate some therapeutic scenarios such as viral annihilation and efficacious HAART therapy. In particular, some mathematical criteria are derived for therapeutic outcomes such as viral persistence and viral annihilation.

Mathematical modeling and simulations of the pathophysiology of Type-2 Diabetes Mellitus

The pathophysiology of Type 2 Diabetes Mellitus (T2DM) is modelled using a coupled system of non-linear deterministic differential equations. An attempt is made to construct to a clinically plausible mathematical model that incorporates the homeostasis associated with endocrinological regulation of glucose and glycogen levels in the human body, by the hormones, insulin and glucagon. The model variables include the concentrations of glucose in the venous blood plasma, the concentration of glycogen in the liver/tissues, the concentration of the hormone glucagon, and the concentration of insulin in the venous blood plasma. The physiological interactions between the model parameters are depicted by clinically measurable rate constants and biophysically quantifiable stoichiometric coefficients. The processes of gluconeogenesis, glycogenolysis, and pulsatile insulin secretion during type 2 diabetes are modelled using plausible auxiliary functions. Investigative computer simulations are performed to elucidate various hypothetical scenarios of glycemia, patho-physiology of T2DM and insulinoma associated hypoglycemia which results from excessive insulin production probably due to a tumor. This study has demonstrated the necessity of simultaneous monitoring of plasma glucose, glucagon, insulin, and glycogen levels in the proper assessment of the pathophysiology of type 2 diabetes and during determination of the therapeutic efficacy of anti-diabetic drugs.

Generalized Newman-Unti expansions☆

Abstract Newman-Unti type expansions for the metric, the spin coefficients and the Riemann tensor components are exhibited for spacetimes which are not necessarily vacuum and in a frame which is not necessarily a Bondi frame. These expansions are given for both the physical spacetime and for the corresponding conformally rescaled (“unphysical”) space.