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  1. ; ; ; ; ( , Scientific African)
    During large scale outbreaks of infectious diseases, it is imperative that media report about the potential risks. Because media reporting plays a vital role in disseminating crucial information about diseases and its associated risk, understanding how media reports could influence individuals’ behavior and its potential impact on disease transmission dynamics is important. A mathematical model within an optimal control framework of a generic disease, accounting for treatment and media reporting of disease-induced deaths is formulated. Due to the complexity of choosing the best media function, our goal is to attempt to address the following research question: what is the effect of the media-induced functional response on mitigating the spread of the disease? Connecting the functional forms to the control problem is an approach that is not very developed in the literature. Thus, this study analyses the effect of different incidence functions on disease transmission, and the qualitative nature of epidemic dynamics by carrying out optimal control analysis using three different contact rates and a media function that is dependent on the number of deaths. Theoretical analyses show that the functional forms of the effective contact rate have no effect on initial disease transmission. Time-dependent controls for treatment and vaccination with a constant effective contact rate are incorporated to determine optimal control strategies. Numerical simulations show the short-term impact of media coverage on mitigating the spread of the disease, and it is observed that with three incidence functions used, the qualitative nature of the controls remains the same. The effective contact rates are graphically shown to have a population-level effect on the disease dynamics as the number of treated and recovered individuals could be significantly different. Finally, it is shown that treatment of infectives should be at its maximum rate for a longer period compared to vaccination, while concurrent implementation of vaccination and treatment is more impactful in mitigating the spread of the disease. Thus, it is imperative that media reports and health policy decision making on infectious diseases are contextualized. 
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    Free, publicly-accessible full text available June 1, 2025
  2. ; ; ; ( , Frontiers in Nutrition)
    Introduction

    Runners competing in races are looking to optimize their performance. In this paper, a runner's performance in a race, such as a marathon, is formulated as an optimal control problem where the controls are: the nutrition intake throughout the race and the propulsion force of the runner. As nutrition is an integral part of successfully running long distance races, it needs to be included in models of running strategies.

     Methods

    We formulate a system of ordinary differential equations to represent the velocity, fat energy, glycogen energy, and nutrition for a runner competing in a long-distance race. The energy compartments represent the energy sources available in the runner's body. We allocate the energy source from which the runner draws, based on how fast the runner is moving. The food consumed during the race is a source term for the nutrition differential equation. With our model, we are investigating strategies to manage the nutrition and propulsion force in order to minimize the running time in a fixed distance race. This requires the solution of a nontrivial singular control problem.

     Results

    As the goal of an optimal control model is to determine the optimal strategy, comparing our results against real data presents a challenge; however, in comparing our results to the world record for the marathon, our results differed by 0.4%, 31 seconds. Per each additional gel consumed, the runner is able to run 0.5 to 0.7 kilometers further in the same amount of time, resulting in a 7.75% increase in taking five 100 calorie gels vs no nutrition.

     Discussion

    Our results confirm the belief that the most effective way to run a race is to run approximately the same pace the entire race without letting one's energies hit zero, by consuming in-race nutrition. While this model does not take all factors into account, we consider it a building block for future models, considering our novel energy representation, and in-race nutrition.

     
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  3. ; ; ; ; ; ; ; ; ; ( , Journal of Mathematical Biology)
    Abstract

    Infectious diseases continue to pose a significant threat to the health of humans globally. While the spread of pathogens transcends geographical boundaries, the management of infectious diseases typically occurs within distinct spatial units, determined by geopolitical boundaries. The allocation of management resources within and across regions (the “governance structure”) can affect epidemiological outcomes considerably, and policy-makers are often confronted with a choice between applying control measures uniformly or differentially across regions. Here, we investigate the extent to which uniform and non-uniform governance structures affect the costs of an infectious disease outbreak in two-patch systems using an optimal control framework. A uniform policy implements control measures with the same time varying rate functions across both patches, while these measures are allowed to differ between the patches in a non-uniform policy. We compare results from two systems of differential equations representing transmission of cholera and Ebola, respectively, to understand the interplay between transmission mode, governance structure and the optimal control of outbreaks. In our case studies, the governance structure has a meaningful impact on the allocation of resources and burden of cases, although the difference in total costs is minimal. Understanding how governance structure affects both the optimal control functions and epidemiological outcomes is crucial for the effective management of infectious diseases going forward.

     
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  4. ; ; ( , PLOS Computational Biology)
    Jenner, Adrianne (Ed.)
    With the recent approval by the FDA of the first disease-modifying drug for Alzheimer’s Disease (AD), personalized medicine will be increasingly important for appropriate management and counseling of patients with AD and those at risk. The growing availability of clinical biomarker data and data-driven computational modeling techniques provide an opportunity for new approaches to individualized AD therapeutic planning. In this paper, we develop a new mathematical model, based on AD cognitive, cerebrospinal fluid (CSF) and MRI biomarkers, to provide a personalized optimal treatment plan for individuals. This model is parameterized by biomarker data from the AD Neuroimaging Initiative (ADNI) cohort, a large multi-institutional database monitoring the natural history of subjects with AD and mild cognitive impairment (MCI). Optimal control theory is used to incorporate time-varying treatment controls and side-effects into the model, based on recent clinical trial data, to provide a personalized treatment regimen with anti-amyloid-beta therapy. In-silico treatment studies were conducted on the approved treatment, aducanumab, as well as on another promising anti-amyloid-beta therapy under evaluation, donanemab. Clinical trial simulations were conducted over both short-term (78 weeks) and long-term (10 years) periods with low-dose (6 mg/kg) and high-dose (10 mg/kg) regimens for aducanumab, and a single-dose regimen (1400 mg) for donanemab. Results confirm those of actual clinical trials showing a large and sustained effect of both aducanumab and donanemab on amyloid beta clearance. The effect on slowing cognitive decline was modest for both treatments, but greater for donanemab. This optimal treatment computational modeling framework can be applied to other single and combination treatments for both prediction and optimization, as well as incorporate new clinical trial data as it becomes available. 
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  5. ; ; ; ; ; ; ; ; ; ; et al ( , Bulletin of Mathematical Biology)
    Abstract Optimal control theory can be a useful tool to identify the best strategies for the management of infectious diseases. In most of the applications to disease control with ordinary differential equations, the objective functional to be optimized is formulated in monetary terms as the sum of intervention costs and the cost associated with the burden of disease. We present alternate formulations that express epidemiological outcomes via health metrics and reframe the problem to include features such as budget constraints and epidemiological targets. These alternate formulations are illustrated with a compartmental cholera model. The alternate formulations permit us to better explore the sensitivity of the optimal control solutions to changes in available budget or the desired epidemiological target. We also discuss some limitations of comprehensive cost assessment in epidemiology. 
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  6. ; ; ; ; ; ; ; ; ; ; et al ( , CBE—Life Sciences Education)
    Kurushima, Jennifer (Ed.)
    Mastery of quantitative skills is increasingly critical for student success in life sciences, but few curricula adequately incorporate quantitative skills. Quantitative Biology at Community Colleges (QB@CC) is designed to address this need by building a grassroots consortium of community college faculty to 1) engage in interdisciplinary partnerships that increase participant confidence in life science, mathematics, and statistics domains; 2) generate and publish a collection of quantitative skills–focused open education resources (OER); and 3) disseminate these OER and pedagogical practices widely, in turn expanding the network. Currently in its third year, QB@CC has recruited 70 faculty into the network and created 20 modules. Modules can be accessed by interested biology and mathematics educators in high school, 2-year, and 4-year institutions. Here, we use survey responses, focus group interviews, and document analyses (principles-focused evaluation) to evaluate the progress in accomplishing these goals midway through the QB@CC program. The QB@CC network provides a model for developing and sustaining an interdisciplinary community that benefits participants and generates valuable resources for the broader community. Similar network-building programs may wish to adopt some of the effective aspects of the QB@CC network model to meet their objectives. 
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  7. ; ; ; ; ( , Ecosphere)
    Abstract

    Adelges tsugaeAnnand, the hemlock woolly adelgid, is an invasive insect pest ofTsuga canadensis(L.) Carriere, eastern hemlock, in the eastern United States. AnA. tsugaeinfestation often results in the death ofT. canadensiswithin years and has caused significant changes to hemlock forests. Cycles inT. canadensishealth andA. tsugaedensities seem to be an important feature inA. tsugaepopulation dynamics in the eastern United States. To investigate mechanisms leading to such cycles, we construct a model composed of systems of ordinary differential equations with time‐dependent parameters to represent seasonality. The model captures the coupled cycles inT. canadensishealth andA. tsugaedensity. We use field data from Virginia to develop the model and to perform parameter estimation. The mechanisms we represent in the model include anA. tsugaedensity‐dependentT. canadensisgrowth rate, aT. canadensishealth‐dependentA. tsugaemortality rate, and a density‐dependentA. tsugaemortality rate, which produce cycles inT. canadensishealth andA. tsugaedensity commonly seen with theA. tsugaesystem in the eastern United States. We test sets of initial conditions to determine the scenarios that will likely lead toT. canadensismortality and explore longer term dynamics of the system. In general, low and highT. canadensishealth initial condition values result in likelyT. canadensismortality whileT. canadensiswith medium health initial condition values are predicted to survive.

     
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  8. ; ; ; ; ; ; ; ( , BMC Public Health)
    Abstract Background

    The development of public health policy is inextricably linked with governance structure. In our increasingly globalized world, human migration and infectious diseases often span multiple administrative jurisdictions that might have different systems of government and divergent management objectives. However, few studies have considered how the allocation of regulatory authority among jurisdictions can affect disease management outcomes.

     Methods

    Here we evaluate the relative merits of decentralized and centralized management by developing and numerically analyzing a two-jurisdictionSIRSmodel that explicitly incorporates migration. In our model, managers choose between vaccination, isolation, medication, border closure, and a travel ban on infected individuals while aiming to minimize either the number of cases or the number of deaths.

     Results

    We consider a variety of scenarios and show how optimal strategies differ for decentralized and centralized management levels. We demonstrate that policies formed in the best interest of individual jurisdictions may not achieve global objectives, and identify situations where locally applied interventions can lead to an overall increase in the numbers of cases and deaths.

     Conclusions

    Our approach underscores the importance of tailoring disease management plans to existing regulatory structures as part of an evidence-based decision framework. Most importantly, we demonstrate that there needs to be a greater consideration of the degree to which governance structure impacts disease outcomes.

     
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  9. ; ; ; ; ; ; ; ; ; ( , Bulletin of Mathematical Biology)
    null (Ed.)
    Abstract Stigma toward people living with HIV/AIDS (PLWHA) has impeded the response to the disease across the world. Widespread stigma leads to poor adherence of preventative measures while also causing PLWHA to avoid testing and care, delaying important treatment. Stigma is clearly a hugely complex construct. However, it can be broken down into components which include internalized stigma (how people with the trait feel about themselves) and enacted stigma (how a community reacts to an individual with the trait). Levels of HIV/AIDS-related stigma are particularly high in sub-Saharan Africa, which contributed to a surge in cases in Kenya during the late twentieth century. Since the early twenty-first century, the United Nations and governments around the world have worked to eliminate stigma from society and resulting public health education campaigns have improved the perception of PLWHA over time, but HIV/AIDS remains a significant problem, particularly in Kenya. We take a data-driven approach to create a time-dependent stigma function that captures both the level of internalized and enacted stigma in the population. We embed this within a compartmental model for HIV dynamics. Since 2000, the population in Kenya has been growing almost exponentially and so we rescale our model system to create a coupled system for HIV prevalence and fraction of individuals that are infected that seek treatment. This allows us to estimate model parameters from published data. We use the model to explore a range of scenarios in which either internalized or enacted stigma levels vary from those predicted by the data. This analysis allows us to understand the potential impact of different public health interventions on key HIV metrics such as prevalence and disease-related death and to see how close Kenya will get to achieving UN goals for these HIV and stigma metrics by 2030. 
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  10. ; ; ; ; ; ; ; ; ( , Ecological Applications)
    null (Ed.)
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