We would like to see whether our strategy could apply in treatment of other types of cancer. We create a model to test whether our strategy outperforms traditional surgery in terms of preventing metastasis of lymphoma. This work is collaborated with SCUT-China.

We made following assumptions to simplify our model: (a) the process of tumorigenesis is irreversible, (b) lymphonode has no effect in metastasis after removal, and (c) tumor must grow to certain sizes and proliferate before metastasis.

We use following variables in our model:

I : Number of Malignant lymphonode
R : Number of Removed lymphonode
S : Number of Normal lymphonode
I0 : Initial Number of malignant lymphonode

We compare following strategies with dynamic epidemic model:

1. Increasing the resistance of normal lymphonode to tumorigenesis

2. Removing malignant lymphonode

3. Inhibit the proliferation of tumor cells

We now know that we can achieve 2 by surgery, and strategy 3 is the potential application field of our research.

We use following probability transition model:

α is the growth rate of tumor cells in terms of size. β measures the growth rate of tumor cells in terms of number. P measures the survival rate of tumor cells during metastasis.

Thus, we have:

λ represents strategy 1, which is roughly proportional to the resistance of normal cells to malignant cells。

We also create the following switch for simulation:

The biological meaning of the switch is that there exists a period of time when metastasis hasn’t been noticed (t < 0.2T). Then a surgery was performed to remove the malignant lymphonode corresponding to strategy . We then performed numerical simulation as below.

We first simulate the control status with parameter below:

I0=10, α=1, β=1, γ=0.05, λ=0.3, p=0.95, T=100

Combing strategy 2 and 3,we have:

I0=10, α=1.5, β=1.5, γ=0.1, λ=0.3, p=0.95, T=100

The result shows that by combing strategy 2 and 3 we successfully delay the metastasis time of tumor cells. We next investigate the effect of p, λ on metastasis:

We create a gradient of p=0.95, 0.94, ..., 0.8 and performed the simulation:

The perform the same analysis for λ:

λ=0.3, 0.31, ..., 0.49, 0.5

The results show that increasing the resistance of normal lymphocyte (increasing λ) and control the survival rate of tumor cells (decreasing p) help to inhibit the metastasis. This will help design our future work.