Numerical Simulations of a Delay Model for Immune System-Tumor Interaction

Abstract

In this paper we consider a system of delay differential equations as a model for the dynamics of tumor-immune system interaction. We carry out a stability analysis of the proposed model. In particular, we show that the system can have up to two steady states: the tumor free steady state, which always exist, and the tumor persistent steady state, which exists only when the relative rate of increase of the tumor cells exceeds the ratio between the natural proliferation rate and the relative death rate of the effector cells. We also determine an upper bound for the delay, such that stability is preserved. Numerical simulations of the system under different parameter values are performed.

Fractional order mathematical modeling of COVID-19 transmission

“…It is very important to study the mathematical models of infectious diseases for a better understanding of their evaluation, existence, stability, and control [1] , [2] , [3] , [37] , [40] , [41] . As the classical approaches of mathematical models do not determine the high degree of accuracy to model these diseases, fractional differential equations were introduced to handle such problems, which have many applications in applied fields like production problems, optimization problem, artificial intelligence, medical diagnoses, robotics, cosmology and many more.…”

Haar wavelet collocation approach for the solution of fractional order COVID-19 model using Caputo derivative

“…Since for the nonlinear problems mostly it is difficult to find their exact solution. Therefore various numerical procedures (methods) have been constructed in literature to deal such like problem, see [31] , [32] , [33] , [34] , [35] , [36] , [41] , [46] . Therefore a famous Haar collocation method is applied to simulate the results via the use of Matlab-16.…”

A mathematical model of Coronavirus Disease (COVID-19) containing asymptomatic and symptomatic classes

“…The main advantage of the operator is that it has a nonlocal and nonsingular kernel. More recently, new advances and studies in fractional differential equations has been published from a mathematical modeling point of view, see recent papers [52] , [19] , [27] , [30] , [46] , [15] , [8] , [28] , [44] , [29] , [7] , [4] , [12] , [11] .…”