Mathematical modeling of combined therapies for treating tumor drug resistance.

Drug resistance is one of the most intractable issues to the targeted therapy for cancer diseases. To explore effective combination therapy schemes, we propose a mathematical model to study the effects of different treatment schemes on the dynamics of cancer cells. Then we characterize the dynamical behavior of the model by finding the equilibrium points and exploring their local stability.

Stationary distribution of a reaction-diffusion hepatitis B virus infection model driven by the Ornstein-Uhlenbeck process.

A reaction-diffusion hepatitis B virus (HBV) infection model based on the mean-reverting Ornstein-Uhlenbeck process is studied in this paper. We demonstrate the existence and uniqueness of the positive solution by constructing the Lyapunov function. The adequate conditions for the solution's stationary distribution were described.

Dynamics analysis of a nonlocal diffusion dengue model.

Due to the unrestricted movement of humans over a wide area, it is important to understand how individuals move between non-adjacent locations in space. In this research, we introduce a nonlocal diffusion introduce for dengue, which is driven by integral operators. First, we use the semigroup theory and continuously Fréchet differentiable to demonstrate the existence, uniqueness, positivity and boundedness of the solution.