Bistability in a model of tumor-immune system interactions with an oncolytic viral therapy

Abstract

<abstract><p>A mathematical model of tumor-immune system interactions with an oncolytic virus therapy for which the immune system plays a twofold role against cancer cells is derived. The immune cells can kill cancer cells but can also eliminate viruses from the therapy. In addition, immune cells can either be stimulated to proliferate or be impaired to reduce their growth by tumor cells. It is shown that if the tumor killing rate by immune cells is above a critical value, the tumor can be eradicated for all sizes, where the critical killing rate depends on whether the immune system is immunosuppressive or proliferative. For a reduced tumor killing rate with an immunosuppressive immune system, that bistability exists in a large parameter space follows from our numerical bifurcation study. Depending on the tumor size, the tumor can either be eradicated or be reduced to a size less than its carrying capacity. However, reducing the viral killing rate by immune cells always increases the effectiveness of the viral therapy. This reduction may be achieved by manipulating certain genes of viruses via genetic engineering or by chemical modification of viral coat proteins to avoid detection by the immune cells.</p></abstract>

The role of tumor activation and inhibition with saturation effects in a mathematical model of tumor and immune system interactions undergoing oncolytic viral therapy

“…Next, if the product 𝛽q of infection rate with virus burst rate is small, then eventually no infected tumor cells and viruses will be present in the tumor microenvironment. The proof of the following proposition is similar to the proof in [10] and is omitted.…”

“…Using mathematical modeling, many researchers have studied tumor-immune system interactions with immunotherapy and/or chemotherapy to provide important insights on tumor evolution and treatment strategies [7][8][9][10][11][12][13][14][15][16][17]. Investigations of effects of discrete delay on the stability of tumor-immune system were performed in [18][19][20][21][22][23].…”

“…Cancers may actively down regulate immune responses elicited against them, leading to immunosupression. To understand the immune activation and inhibition by cancer cells on OVT success, we studied a simple mathematical model in [10] where cancer either eliciting or suppressing immune cells was modeled by a single parameter with a simple mass action law to describe tumor suppression or evocation. However, cancer suppression and activation are likely to be limited by cancer cells [11,40], and these mechanisms on immune cells can work simultaneously [37,38].…”

“…However, cancer suppression and activation are likely to be limited by cancer cells [11,40], and these mechanisms on immune cells can work simultaneously [37,38]. To model these mechanisms more accurately, in the present study, we incorporate saturation effects of cancer cells into the tumor-immune system interactions, and the cancer cells can stimulate and inhibit immune cells simultaneously instead of separately as in [10]. In particular, based on [7], a single parameter with only one term in [10] is extended to four parameters with two expressions to describe the action of cancer cells on immune cells more precisely.…”

On a Mathematical Model of Tumor‐Immune Interaction with a Piecewise Differential and Integral Operator

“…Kuznetsov et al [11] developed a tumor-immune interaction mathematical model and described the response of effector cells to the growth of an immunogenic tumor. There are many other studies made on the tumor-immune interaction (see for instance [12][13][14][15][16]).…”