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[...]a review paper on quantitative characterization of animal social organization with applications for epidemiological modeling is provided. [...]in a review paper, Voelkl introduced network analysis as a tool to characterize the social organization of animal groups and populations. [...]we thank the Editor-in-Chief of MBE, Professor Yang Kuang, and the Editor Assistant, for their professional and technical support and for making this special issue possible.

Optimal control methods are applied to a deterministic mathematical model to characterize the factors contributing to the replacement of hospital-acquired methicillin-resistant Staphylococcus aureus (HA-MRSA) with community-acquired methicillin-resistant Staphylococcus aureus (CA-MRSA), and quantify the effectiveness of three interventions aimed at limiting the spread of CA-MRSA in healthcare settings. Characterizations of the optimal control strategies are established, and numerical simulations are provided to illustrate the results.

We construct a West Nile virus epidemic model that includes the interaction between the bird hosts and mosquito vectors, mosquito life stages (eggs, larvae, adults), and the dynamics of both larvicide and adulticide. We derive the basic reproduction number for the epidemic as the spectral radius of the next generation matrix. We formulate two impulsive optimal control problems which seek to balance the cost of insecticide applications (both the timing and application level) with the benefit of (1) vector control: reducing the number of mosquitoes or (2) disease control: reducing the disease burden. We reformulate these impulsive optimal control problems as nonlinear optimization problems and derive associated necessary conditions for the optimal controls. Numerical simulations are used to address three questions: How does the control and its impact on the system vary with the objective type? Is it beneficial to optimize the treatment timing? How does the control and its impact on the population vary with the type of pesticide used?

Harvesting wild plants for non-timber forest products (NTFPs) can be ecologically sustainable–without long-term consequences to the dynamics of targeted and associated species–but it may not be economically satisfying because it fails to provide enough revenues for local people over time. In several cases, the same species can be harvested for NTFP and also logged for timber. Three decades of studies on the sustainability of NTFP harvest for local people’s livelihood have failed to successfully integrate these socio-economic and ecological factors. We apply optimal control theory to investigate optimal strategies for the combinations of non-lethal (e.g., NTFP) and lethal (e.g., timber) harvest that minimize the cost of harvesting while maximizing the benefits (revenue) that accrue to harvesters and the conservation value of harvested ecosystems. Optimal harvesting strategies include starting with non-lethal NTFP harvest and postponing lethal timber harvesting to begin after a few years. We clearly demonstrate that slow growth species have lower optimal harvesting rates, objective functional values and profits than fast growth species. However, contrary to expectation, the effect of species lifespan on optimal harvesting rates was weak suggesting that life history is a better indicator of species resilience to harvest than lifespan. Overall, lethal or nonlethal harvest rates must be <40 % to ensure optimality. This optimal rate is lower than commonly reported sustainable harvest rates for non-timber forest products.

We are considering an optimal control problem for a type of hybrid system involving ordinary differential equations and a discrete time feature. One state variable has dynamics in only one season of the year and has a jump condition to obtain the initial condition for that corresponding season in the next year. The other state variable has continuous dynamics. Given a general objective functional, existence, necessary conditions and uniqueness for an optimal control are established. We apply our approach to a tick-transmitted disease model with age structure in which the tick dynamics changes seasonally while hosts have continuous dynamics. The goal is to maximize disease-free ticks and minimize infected ticks through an optimal control strategy of treatment with acaricide. Numerical examples are given to illustrate the results.

This paper highlights a parallel between the forward backward sweeping method for optimal control and deep learning training procedures. We reformulate a classical optimal control problem, constrained by a differential equation system, into an optimization framework that uses neural networks to represent control variables. We demonstrate that this deep learning method adheres to Pontryagin Maximum Principle and mitigates numerical instabilities by employing backward propagation instead of a backward sweep for the adjoint equations. As a case study, we solve an optimal control problem to find the optimal combination of immunotherapy and chemotherapy. Our approach holds significant potential across various fields, including epidemiology, ecological modeling, engineering, and financial mathematics, where optimal control under complex dynamic constraints is crucial.

In this dissertation, we investigate optimal control of hybrid differential equations and elliptic partial differential equations with two biological applications. We prove the existence of an optimal control for which the objective functional is maximized. The goal is to characterize the optimal control in terms of the solution of the optimality system. The optimality system consists of the state equations coupled with the adjoint equations. To obtain the optimality system we differentiate the objective functional with respect to the control. This process is applied to studying two problems: one is a type of hybrid system involving ordinary differential equations and a discrete time feature. We apply our approach to a tick-transmitted disease model in which the tick dynamics changes seasonally while hosts have continuous dynamics. The goal is to maximize disease-free ticks and minimize infected ticks through an optimal control strategy of treatment with acaricide. The other is a semi-linear elliptic partial differential equation model for fishery harvesting. We consider two objective functionals: maximizing the yield and minimizing the cost or variation in the fishing effort (control). Existence, necessary conditions and uniqueness for the optimal control for both problems are established. Numerical examples are given to illustrate the results.

We study the optimal control problem of a free boundary PDE model describing the growth of multilayered tumor tissue in vitro. We seek the optimal amount of tumor growth inhibitor that simultaneously minimizes the thickness of the tumor tissue and mitigates side effects. The existence of an optimal control is established, and the uniqueness and characterization of the optimal control are investigated. Numerical simulations are presented for some scenarios, including the steady-state and parabolic cases.

Artificial intelligence (AI) can potentially transform global health, but algorithmic bias can exacerbate social inequities and disparity. Trustworthy AI entails the intentional design to ensure equity and mitigate potential biases. To advance trustworthy AI in global health, we convened a workshop on Fairness in Machine Intelligence for Global Health (FairMI4GH). The event brought together a global mix of experts from various disciplines, community health practitioners, policymakers, and more. Topics covered included managing AI bias in socio-technical systems, AI's potential impacts on global health, and balancing data privacy with transparency. Panel discussions examined the cultural, political, and ethical dimensions of AI in global health. FairMI4GH aimed to stimulate dialogue, facilitate knowledge transfer, and spark innovative solutions. Drawing from NIST's AI Risk Management Framework, it provided suggestions for handling AI risks and biases. The need to mitigate data biases from the research design stage, adopt a human-centered approach, and advocate for AI transparency was recognized. Challenges such as updating legal frameworks, managing cross-border data sharing, and motivating developers to reduce bias were acknowledged. The event emphasized the necessity of diverse viewpoints and multi-dimensional dialogue for creating a fair and ethical AI framework for equitable global health.

Delamination is one of the major damages associated with drilling carbon fiber-reinforced plastics (CFRP), Peel-up and Push-out are two recognizable delamination mechanisms, while drilling without using a back-up plate under the workpiece complicates the delamination mechanism even more. Minimizing delamination is dependent on many factors such as cutting parameters, geometry and type of drill bits used. The objective of this study is to present a new approach to measure the equivalent adjusted delamination factor ( F e d a ) when drilling unidirectional CFRP laminates without using a back-up plate and comparing it experimentally and numerically with conventional delamination factor ( F d ) and adjusted delamination factor ( F d a ). A polycrystalline diamond (PCD) twist drill and a special diamond coated double point angle drill was used for drilling in this study. The 3D finite element model was developed in ANSYS-Explicit to simulate the drilling process using the ply-based modeling method instead of a conventional zone-based concept. Experimental drilling validation process was implemented by utilizing a CNC machining center. Results show that the F e d a obtained is suitable to estimate the drilling induced damages, damage analysis shows that good agreements were obtained from the experiments and finite element method (FEM) simulation, while the special diamond coated double point angle drill seemed to provide a better hole quality, and drilling induced damage is highly affected by feed rate which is considered one of the important parameter.