On the Fitness of Predators with Prey-Induced Dispersal in a Habitat with Spatial Heterogeneity.

This study considers a situation in which a predator can change its dispersal rate according to its satisfaction with foraging prey in a predator-prey interaction. However, since it is impossible to accurately determine the magnitude of the density of prey that is favorable to a predator's survival in an area, the predator determines the movement rate through inaccurate judgment. In this situation, we investigate the effect of the predator's decision about its movement on fitness. To achieve our goal, we consider a predator-prey model with nonuniform predator dispersal, called prey-induced dispersal (PYID), in which the spread of predators is small when the prey density is larger than a certain value, and when the prey density is smaller than a particular value, a large spread of predators occurs. To understand how PYID affects the dynamics and coexistence of the system in a spatially heterogeneous region, we examine a model with Holling-type II functional responses under no-flux boundary conditions wherein the predators move according to the PYID. We study the local stability of the semitrivial solution of models with PYID and linear dispersal where the predator is absent. Furthermore, we investigate the local/global bifurcation from the semitrivial solution of models with two different dispersals. We conclude that in most cases, nonuniform dispersal of predators following PYID promotes predator fitness; however, there is a case in which PYID does not increase predator fitness. If a predator's satisfaction degree regarding the prey density is higher than a certain level, there may exist a case that is not beneficial for predators in terms of their fitness. However, if the satisfaction level of predators regarding prey density is relatively low, predators following PYID will take advantage of fitness. More precisely, if predators are dissatisfied with the amount of prey in a region and move quickly, even for abundant prey density, they may not benefit from PYID. Meanwhile, if predators change their motility when they are appropriately satisfied with the amount of prey, they will obtain a survival advantage. We obtain the results by analyzing an eigenvalue problem at the semitrivial solution from the linearized operators derived from the models.

Co-Evolution of Predator-Prey Ecosystems by Reinforcement Learning Agents.

The problem of finding adequate population models in ecology is important for understanding essential aspects of their dynamic nature. Since analyzing and accurately predicting the intelligent adaptation of multiple species is difficult due to their complex interactions, the study of population dynamics still remains a challenging task in computational biology. In this paper, we use a modern deep reinforcement learning (RL) approach to explore a new avenue for understanding predator-prey ecosystems. Recently, reinforcement learning methods have achieved impressive results in areas, such as games and robotics. RL agents generally focus on building strategies for taking actions in an environment in order to maximize their expected returns. Here we frame the co-evolution of predators and preys in an ecosystem as allowing agents to learn and evolve toward better ones in a manner appropriate for multi-agent reinforcement learning. Recent significant advancements in reinforcement learning allow for new perspectives on these types of ecological issues. Our simulation results show that throughout the scenarios with RL agents, predators can achieve a reasonable level of sustainability, along with their preys.

Intraguild predation with evolutionary dispersal in a spatially heterogeneous environment.

In many cases, the motility of species in a certain region can depend on the conditions of the local habitat, such as the availability of food and other resources for survival. For example, if resources are insufficient, the motility rate of a species is high, as they move in search of food. In this paper, we present intraguild predation (IGP) models with a nonuniform random dispersal, called starvation-driven diffusion, which is affected by the local conditions of habitats in heterogeneous environments. We consider a Lotka-Volterra-type model incorporating such dispersals, to understand how a nonuniform random dispersal affects the fitness of each species in a heterogeneous region. Our conclusion is that a nonuniform dispersal increases the fitness of species in a spatially heterogeneous environment. The results are obtained through an eigenvalue analysis of the semi-trivial steady state solutions for the linearized operator derived from the model with nonuniform random diffusion on IGPrey and IGPredator, respectively. Finally, a simulation and its biological interpretations are presented based on our results.

Investigation of nonlinear epidemiological models for analyzing and controlling the MERS outbreak in Korea.

Much concern has arisen regarding serious epidemics due to the Middle East Respiratory Syndrome (MERS) coronavirus. The first MERS case of Korea was reported on 20 May 2015, and since then, the MERS outbreak in Korea has resulted in hundreds of confirmed cases and tens of deaths. Deadly infectious diseases such as MERS have significant direct and indirect social impacts, which include disease-induced mortality and economic losses. Also, a delayed response to the outbreak and underestimating its danger can further aggravate the situation. Hence, an analysis and establishing efficient strategies for preventing the propagation of MERS is a very important and urgent issue. In this paper, we propose a class of nonlinear susceptible-infectious-quarantined (SIQ) models for analyzing and controlling the MERS outbreak in Korea. For the SIQ based ordinary differential equation (ODE) model, we perform the task of parameter estimation, and apply optimal control theory to the controlled SIQ model, with the goal of minimizing the infectious compartment population and the cost of implementing the quarantine and isolation strategies. Simulation results show that the proposed SIQ model can explain the observed data for the confirmed cases and the quarantined cases in the MERS outbreak very well, and the number of the MERS cases can be controlled reasonably well via the optimal control approach.

A risk-induced dispersal strategy of the infected population for a disease-free state in the SIS epidemic model.

This article proposes a dispersal strategy for infected individuals in a spatial susceptible-infected-susceptible (SIS) epidemic model. The presence of spatial heterogeneity and the movement of individuals play crucial roles in determining the persistence and eradication of infectious diseases. To capture these dynamics, we introduce a moving strategy called risk-induced dispersal (RID) for infected individuals in a continuous-time patch model of the SIS epidemic. First, we establish a continuous-time n-patch model and verify that the RID strategy is an effective approach for attaining a disease-free state. This is substantiated through simulations conducted on 7-patch models and analytical results derived from 2-patch models. Second, we extend our analysis by adapting the patch model into a diffusive epidemic model. This extension allows us to explore further the impact of the RID movement strategy on disease transmission and control. We validate our results through simulations, which provide the effects of the RID dispersal strategy.

Predation-induced dispersal toward fitness for predator invasion in predator-prey models.

In this paper, we consider a predator-prey model with nonuniform predator dispersal, called predation-induced dispersal (PID), which represents predator motility depending on the maximal predation rate and the predator death rate in a spatially heterogeneous region. We study the local stability of the semitrivial steady state when predators are absent for models with PID and linear dispersal. We then investigate the local/global bifurcation from the semitrivial steady state of these models. Finally, we compare the results of the model with PID to the results of the model with linear dispersal. We conclude that the nonuniform dispersal of predators obeying PID increases fitness for predator invasion when rare; thus, predators with PID can invade a region with an increased probability even in cases wherein predators dispersed linearly cannot invade a certain region. Based on the results, we provide an ecological interpretation with the simulations.

The impact factors of the risk index and diffusive dynamics of a SIS free boundary model.

To discuss the impact factors on the spread of infectious diseases, we study a free boundary problem describing a SIS (susceptible-infected-susceptible) model in a heterogeneous environment. Firstly, the existence and uniqueness of the global solution are given. Then the basic reproduction number related to time is defined, and a spreading-vanishing dichotomy of infectious diseases is obtained. The impacts of the diffusion rate of infected individuals, expanding capability, and the scope and scale of initial infection on the spreading and vanishing of infectious disease are analyzed. Numerical simulations are given to show that the large expanding capability is unfavorable to the prevention and control of the disease.

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.