Immunotherapy with Interleukin-2: A Study Based on Mathematical Modeling

Abstract

The role of interleukin-2 (IL-2) in tumor dynamics is illustrated through mathematical modeling, using delay differential equations with a discrete time delay (a modified version of the Kirshner-Panetta model). Theoretical analysis gives an expression for the discrete time delay and the length of the time delay to preserve stability. Numerical analysis shows that interleukin-2 alone can cause the tumor cell population to regress.

Stability Analysis of Nonlinear Time–Delayed Systems with Application to Biological Models

“…A mathematical model of the Lotka-Volterra type (Melief, 2005;d'Onofrio, 2005) which captures the nonlinearity of tumor-immune-cell interactions is adopted and further studied in this paper. Predator-prey equations have accommodated this problem well (Bell, 1973) and have been a subject of active investigation (Andrew et al, 2007;Zhivkov and Waniewski, 2003;Banerjee, 2008).…”

Bifurcation analysis of a delayed mathematical model for tumor growth

“…Their model also exhibits Hopf bifurcation through periodic solutions. Banerjee [13], studied the modified model of Kirschner and Panetta [4], and introduce the discrete time delay in the proliferation of effector cells due to interaction with interleukin-2 (IL-2) to investigate the effect of time delay during immunotherapy with IL-2. Galach [25] studied a simplified mathematical model of Kuznetsov et al [5] for tumor cells and immune effector cells with discrete time delay.…”

“…Keeping this information in our mind, we modify the model of de Pillis and Radunskaya [3], by introduce a discrete time lag in the interaction between host cells and the tumor cells. The study of tumor growth with discrete time delay has been of remarkable interest of researchers for a long period of time [10,13,14,16,19,[21][22][23][24][25]29,39]. For instance, it has been shown that a time lag, introduced in the cancerous cells response to change in their environment, influence the growth of cancers: shorter the delay, stronger the tumor [10].…”

Bağışıklık Sistemi Etkisi Altında Tümör Büyümesinin Modellenmesi

“…Birçok araştırmacı tümör-bağışıklık sistemi etkileşiminin modellenmesinde Lotka-Volterra terimler ve Verhulst (Lojistik) terimler kullanmışlardır [3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Gatenby [3] tümör hücreleriyle, tümör hücrelerinin ortaya çıktığı konak hücreler arasındaki rekabeti standart Lotka-Volterra türler arası rekabet modelini kullanarak modellemiştir.…”