Inkyung Ahn

Coexistence theorem of steady states for nonlinear self-cross diffusion systems with competitive dynamics

In this paper, we discuss the existence of positive solutions to certain nonlinear elliptic systems representing competitive interaction with self-cross diffusions between two species. The method employed is the fixed point index theory in a positive cone. Sufficient conditions for the existence of positive solutions are provided.

Coexistence of a one-prey two-predators model with ratio-dependent functional responses

Abstract We examine the positive coexistence of one prey and two competing predators in an interacting system with ratio-dependent functional responses under a hostile environment. Furthermore, we examine the extinction conditions for all three interacting species and for one or two of the three species. In addition, we present the biological interpretation and simulations based on the result. The methods employed are a comparison argument for the elliptic problem and the fixed-point theory applied to a positive cone on a Banach space.

Drug scheduling of cancer chemotherapy based on natural actor-critic approach.

Recently, reinforcement learning methods have drawn significant interests in the area of artificial intelligence, and have been successfully applied to various decision-making problems. In this paper, we study the applicability of the NAC (natural actor-critic) approach, a state-of-the-art reinforcement learning method, to the drug scheduling of cancer chemotherapy for an ODE (ordinary differential equation)-based tumor growth model. ODE-based cancer dynamics modeling is an active research area, and many different mathematical models have been proposed. Among these, we use the model proposed by de Pillis and Radunskaya (2003), which considers the growth of tumor cells and their interaction with normal cells and immune cells. The NAC approach is applied to this ODE model with the goal of minimizing the tumor cell population and the drug amount while maintaining the adequate population levels of normal cells and immune cells. In the framework of the NAC approach, the drug dose is regarded as the control input, and the reward signal is defined as a function of the control input and the cell populations of tumor cells, normal cells, and immune cells. According to the control policy found by the NAC approach, effective drug scheduling in cancer chemotherapy for the considered scenarios has turned out to be close to the strategy of continuing drug injection from the beginning until an appropriate time. Also, simulation results showed that the NAC approach can yield better performance than conventional pulsed chemotherapy.

POSITIVE COEXISTENCE FOR A SIMPLE FOOD CHAIN MODEL WITH RATIO-DEPENDENT FUNCTIONAL RESPONSE AND CROSS-DIFFUSION

The positive coexistence of a simple food chain model with ratio-dependent functional response and cross-difiusion is dis- cussed. Especially, when a cross-difiusion is small enough, the exis- tence of positive solutions of the system concerned can be expected. The extinction conditions for all three interacting species and for one or two of three species are studied. Moreover, when a cross- difiusion is su-ciently large, the extinction of prey species with cross-difiusion interaction to predator occurs. The method em- ployed is the comparison argument for elliptic problem and flxed point theory in a positive cone on a Banach space.

Strong competition model with non-uniform dispersal in a heterogeneous environment

Abstract In this study, a strong competition model was considered between two species in a heterogeneous environment. For a system with two different constant diffusion rates for each competitor, the fast diffuser can be selected evolutionally under suitable assumptions if the competing interaction between the species is strong. We also claim that a strongly interacting competition leads to a more evolutionary selection than that with the same population dynamics if a species moves with a certain non-uniform dispersal. Furthermore, species with a certain non-uniform dispersal have a competitive advantage over linear random diffusers. In addition, a species with highly sensitive dispersal response to the environment may survive. These strongly competitive advantages were demonstrated by investigating the stability of semi-trivial solutions of the system with non-uniform dispersal and comparing it to the conditions of the model with constant diffusion.

UNIQUENESS OF POSITIVE STEADY STATES FOR WEAK COMPETITION MODELS WITH SELF-CROSS DIFFUSIONS

In this paper, we investigate the uniqueness of positive solutions to weak competition models with self-cross diffusion rates under homogeneous Dirichlet boundary conditions. The methods employed are upper-lower solution technique and the variational characterization of eigenvalues.