Resource allocation in a PDE ecosystem model.

The effects of habitat heterogeneity on a diffusing population are investigated here. We formulate a reaction-diffusion system of partial differential equations to analyze the effect of resource allocation in an ecosystem with resource having its own dynamics in space and time. We show a priori estimates to prove the existence of state solutions given a control. We formulate an optimal control problem of our ecosystem model such that the abundance of a single species is maximized while minimizing the cost of inflow resource allocation. In addition, we show the existence and uniqueness of the optimal control as well as the optimal control characterization. We also establish the existence of an optimal intermediate diffusion rate. Moreover, we illustrate several numerical simulations with Dirichlet and Neumann boundary conditions with the space domain in 1D and 2D.

The optimal controlling strategy on a dispersing population in a two-patch system: Experimental and theoretical perspectives.

Invasive species, disease vectors, and pathogens are significant threats to biodiversity, ecosystem function and services, and human health. Understanding the optimal management strategy, which maximizes the effectiveness is crucial. Despite an abundance of theoretical work has conducted on projecting the optimal allocation strategy, almost no empirical work has been performed to validate the theory. We first used a consumer-resource model to simulate a series of allocation fractions of controlling treatment to determine the optimal controlling strategy. Further, we conducted rigorous laboratory experiments using spatially diffusing laboratory populations of yeast to verify our mathematical results. We found consistent results that: (1) When population growth is limited by the local resource, the controlling priority should be given to the areas with higher concentration of resource; (2) When population growth is not limited by the resource concentration, the best strategy is to allocate equal amount of controlling efforts among the regions; (3) With restricted budget, it is more efficient to prioritize the controlling effects to the areas with high population abundance, otherwise, it is better to control equally among the regions. The new theory, which was tested by laboratory experiments, will reveal new opportunities for future field interventions, thereby informing subsequent biological decision-making.

Comparing intervention strategies for reducing Clostridioides difficile transmission in acute healthcare settings: an agent-based modeling study.

BACKGROUND: Clostridioides difficile infection (CDI) is one of the most common healthcare infections. Common strategies aiming at controlling CDI include antibiotic stewardship, environmental decontamination, and improved hand hygiene and contact precautions. Mathematical models provide a framework to evaluate control strategies. Our objective is to evaluate the effectiveness of control strategies in decreasing C. difficile colonization and infection using an agent-based model in an acute healthcare setting. METHODS: We developed an agent-based model that simulates the transmission of C. difficile in medical wards. This model explicitly incorporates healthcare workers (HCWs) as vectors of transmission, tracks individual patient antibiotic histories, incorporates varying risk levels of antibiotics with respect to CDI susceptibility, and tracks contamination levels of ward rooms by C. difficile. Interventions include two forms of antimicrobial stewardship, increased environmental decontamination through room cleaning, improved HCW compliance, and a preliminary assessment of vaccination. RESULTS: Increased HCW compliance with CDI patients was ranked as the most effective intervention in decreasing colonizations, with reductions up to 56%. Antibiotic stewardship practices were highly ranked after contact precaution compliance. Vaccination and reduction of high-risk antibiotics were the most effective intervention in decreasing CDI. Vaccination reduced CDI cases to up to 90%, and the reduction of high-risk antibiotics decreased CDI cases up to 23%. CONCLUSIONS: Overall, interventions that decrease patient susceptibility to colonization by C. difficile, such as antibiotic stewardship, were the most effective interventions in reducing both colonizations and CDI cases.

Antimicrobial Stewardship and Environmental Decontamination for the Control of Clostridium difficile Transmission in Healthcare Settings.

We implement an agent-based model for Clostridium difficile transmission in hospitals that accounts for several processes and individual factors including environmental and antibiotic heterogeneity in order to evaluate the efficacy of various control measures aimed at reducing environmental contamination and mitigating the effects of antibiotic use on transmission. In particular, we account for local contamination levels that contribute to the probability of colonization and we account for both the number and type of antibiotic treatments given to patients. Simulations illustrate the relative efficacy of several strategies for the reduction of nosocomial colonizations and nosocomial diseases.