Quantifying trade-offs between therapeutic efficacy and resistance dissemination for enrofloxacin dose regimens in cattle.

The use of antimicrobial drugs in food-producing animals increases the selection pressure on pathogenic and commensal bacteria to become resistant. This study aims to evaluate the existence of trade-offs between treatment effectiveness, cost, and the dissemination of resistance in gut commensal bacteria. We developed a within-host ordinary differential equation model to track the dynamics of antimicrobial drug concentrations and bacterial populations in the site of infection (lung) and the gut. The model was parameterized to represent enrofloxacin treatment for bovine respiratory disease (BRD) caused by Pastereulla multocida in cattle. Three approved enrofloxacin dosing regimens were compared for their effects on resistance on P. multocida and commensal E. coli: 12.5 mg/kg and 7.5 mg/kg as a single dose, and 5 mg/kg as three doses. Additionally, we explored non-approved regimes. Our results indicated that both 12.5 mg/kg and 7.5 mg/kg as a single dose scenario increased the most the treatment costs and prevalence of P. multocida resistance in the lungs, while 5 mg/kg as three doses increased resistance in commensal E. coli bacteria in the gut the most out of the approved scenarios. A proposed scenario (7.5 mg/kg, two doses 24 hours apart) showed low economic costs, minimal P. multocida, and moderate effects on resistant E. coli. Overall, the scenarios that decrease P. multocida, including resistant P. multocida did not coincide with the scenarios that decrease resistant E. coli the most, suggesting a trade-off between both outcomes. The sensitivity analysis indicates that bacterial populations were the most sensitive to drug conversion factors into plasma (ß), elimination of the drug from the colon (υ), fifty percent sensitive bacteria (P. multocida) killing effect (Ls50), fifty percent of bacteria (E. coli) above ECOFF killing effect (Cr50), and net drug transfer rate in the lung (γ) parameters.

Modeling county level COVID-19 transmission in the greater St. Louis area: Challenges of uncertainty and identifiability when fitting mechanistic models to time-varying processes.

We use a compartmental model with a time-varying transmission parameter to describe county level COVID-19 transmission in the greater St. Louis area of Missouri and investigate the challenges in fitting such a model to time-varying processes. We fit this model to synthetic and real confirmed case and hospital discharge data from May to December 2020 and calculate uncertainties in the resulting parameter estimates. We also explore non-identifiability within the estimated parameter set. We find that the death rate of infectious non-hospitalized individuals, the testing parameter and the initial number of exposed individuals are not identifiable based on an investigation of correlation coefficients between pairs of parameter estimates. We also explore how this non-identifiability ties back into uncertainties in the estimated parameters and find that it inflates uncertainty in the estimates of our time-varying transmission parameter. However, we do find that R0 is not highly affected by non-identifiability of its constituent components and the uncertainties associated with the quantity are smaller than those of the estimated parameters. Parameter values estimated from data will always be associated with some uncertainty and our work highlights the importance of conducting these analyses when fitting such models to real data. Exploring identifiability and uncertainty is crucial in revealing how much we can trust the parameter estimates.

Structural instability and linear allocation control in generalized models of substance use disorder.

Substance use disorder (SUD) is a complex disease involving nontrivial biological, psychological, environmental, and social factors. While many mathematical studies have proposed compartmental models for SUD, almost all of these exclusively model new cases as the result of an infectious process, neglecting any SUD that was primarily developed in social isolation. While these decisions were likely made to facilitate mathematical analysis, isolated SUD development is critical for the most common substances of abuse today, including opioid use disorder developed through prescription use and alcoholism developed primarily due to genetic factors or stress, depression, and other psychological factors. In this paper we will demonstrate that even a simple infectious disease model is structurally unstable with respect to a linear perturbation in the infection term - precisely the sort of term necessary to model SUD development in isolation. This implies that models of SUD which exclusively treat problematic substance use as an infectious disease will have misleading dynamics whenever a non-trivial rate of isolated SUD development exists in actuality. As we will show, linearly perturbed SUD models do not have a use disorder-free equilibrium. To investigate management strategies, we implement optimal control techniques with the goal of minimizing the number of SUD cases over time.

Geographic disparities and predictors of COVID-19 vaccination in Missouri: a retrospective ecological study.

Background: Limited information is available on geographic disparities of COVID-19 vaccination in Missouri and yet this information is essential for guiding efforts to improve vaccination coverage. Therefore, the objectives of this study were to (a) investigate geographic disparities in the proportion of the population vaccinated against COVID-19 in Missouri and (b) identify socioeconomic and demographic predictors of the identified disparities. Methods: The COVID-19 vaccination data for time period January 1 to December 31, 2021 were obtained from the Missouri Department of Health. County-level data on socioeconomic and demographic factors were downloaded from the 2020 American Community Survey. Proportions of county population vaccinated against COVID-19 were computed and displayed on choropleth maps. Global ordinary least square regression model and local geographically weighted regression model were used to identify predictors of proportions of COVID-19 vaccinated population. Results: Counties located in eastern Missouri tended to have high proportions of COVID-19 vaccinated population while low proportions were observed in the southernmost part of the state. Counties with low proportions of population vaccinated against COVID-19 tended to have high percentages of Hispanic/Latino population (p = 0.046), individuals living below the poverty level (p = 0.049), and uninsured (p = 0.015) populations. The strength of association between proportion of COVID-19 vaccinated population and percentage of Hispanic/Latino population varied by geographic location. Conclusion: The study findings confirm geographic disparities of proportions of COVID-19 vaccinated population in Missouri. Study findings are useful for guiding programs geared at improving vaccination coverage and uptake by targeting resources to areas with low proportions of vaccinated individuals.

Modeling impact of vaccination on COVID-19 dynamics in St. Louis.

The region of St. Louis, Missouri, has displayed a high level of heterogeneity in COVID-19 cases, hospitalization, and vaccination coverage. We investigate how human mobility, vaccination, and time-varying transmission rates influenced SARS-CoV-2 transmission in five counties in the St. Louis area. A COVID-19 model with a system of ordinary differential equations was developed to illustrate the dynamics with a fully vaccinated class. Using the weekly number of vaccinations, cases, and hospitalization data from five counties in the greater St. Louis area in 2021, parameter estimation for the model was completed. The transmission coefficients for each county changed four times in that year to fit the model and the changing behaviour. We predicted the changes in disease spread under scenarios with increased vaccination coverage. SafeGraph local movement data were used to connect the forces of infection across various counties.

The effect of governance structures on optimal control of two-patch epidemic models.

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.

Analyzing the effect of restrictions on the COVID-19 outbreak for some US states.

The ongoing pandemic disease COVID­19 has caused worldwide social and financial disruption. As many countries are engaged in designing vaccines, the harmful second and third waves of COVID­19 have already appeared in many countries. To investigate changes in transmission rates and the effect of social distancing in the USA, we formulate a system of ordinary differential equations using data of confirmed cases and deaths in these states: California, Texas, Florida, Georgia, Illinois, Louisiana, Michigan, and Missouri. Our models and their parameter estimations show social distancing can reduce the transmission of COVID­19 by 60% to 90%. Thus, obeying the movement restriction rules is crucial in reducing the magnitude of the outbreak waves. This study also estimates the percentage of people who were not social distancing ranges between 10% and 18% in these states. Our analysis shows the management restrictions taken by these states do not slow the disease progression enough to contain the outbreak.

Optimally controlling nutrition and propulsion force in a long distance running race.

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.

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.

Toward an optimal contraception dosing strategy.

Anovulation refers to a menstrual cycle characterized by the absence of ovulation. Exogenous hormones such as synthetic progesterone and estrogen have been used to attain this state to achieve contraception. However, large doses are associated with adverse effects such as increased risk for thrombosis and myocardial infarction. This study utilizes optimal control theory on a modified menstrual cycle model to determine the minimum total exogenous estrogen/progesterone dose, and timing of administration to induce anovulation. The mathematical model correctly predicts the mean daily levels of pituitary hormones LH and FSH, and ovarian hormones E2, P4, and Inh throughout a normal menstrual cycle and reflects the reduction in these hormone levels caused by exogenous estrogen and/or progesterone. Results show that it is possible to reduce the total dose by 92% in estrogen monotherapy, 43% in progesterone monotherapy, and that it is most effective to deliver the estrogen contraceptive in the mid follicular phase. Finally, we show that by combining estrogen and progesterone the dose can be lowered even more. These results may give clinicians insights into optimal formulations and schedule of therapy that can suppress ovulation.

Quantitative Biology at Community Colleges, a Network of Biology and Mathematics Faculty Focused on Improving Numerical and Quantitative Skills of Students.

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.

Reframing Optimal Control Problems for Infectious Disease Management in Low-Income Countries.

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.

Extensions of mean-field approximations for environmentally-transmitted pathogen networks.

Many pathogens spread via environmental transmission, without requiring host-to-host direct contact. While models for environmental transmission exist, many are simply constructed intuitively with structures analogous to standard models for direct transmission. As model insights are generally sensitive to the underlying model assumptions, it is important that we are able understand the details and consequences of these assumptions. We construct a simple network model for an environmentally-transmitted pathogen and rigorously derive systems of ordinary differential equations (ODEs) based on different assumptions. We explore two key assumptions, namely homogeneity and independence, and demonstrate that relaxing these assumptions can lead to more accurate ODE approximations. We compare these ODE models to a stochastic implementation of the network model over a variety of parameters and network structures, demonstrating that with fewer restrictive assumptions we are able to achieve higher accuracy in our approximations and highlighting more precisely the errors produced by each assumption. We show that less restrictive assumptions lead to more complicated systems of ODEs and the potential for unstable solutions. Due to the rigour of our derivation, we are able to identify the reason behind these errors and propose potential resolutions.

The effect of changing COVID-19 restrictions on the transmission rate in a veterinary clinic.

With the declaration of the COVID-19 pandemic by the World Health Organization on March 11, 2020, the University of Tennessee College of Veterinary Medicine (UTCVM), like other institutions, restructured their services to reduce the potential spread of the COVID-19 virus while simultaneously providing critical and essential veterinary services. A mathematical model was developed to predict the change in the level of possible COVID-19 infections due to the increased number of potential contacts within the UTCVM hospital. A system of ordinary differential equations with different compartments for UTCVM individuals and the Knox county population was formulated to show the dynamics of transmission and the number of confirmed cases. Key transmission rates in the model were estimated using COVID-19 case data from the surrounding county and UTCVM personnel. Simulations from this model show the increasing number of COVID-19 cases among UTCVM personnel as the number of daily clients and the number of veterinary staff in the clinic are increased. We also investigate how changes within the Knox county community impact the UTCVM hospital. These scenarios show the importance of understanding the effects of re-opening scenarios in veterinary teaching hospitals.

Modeling the effects of size-dependent harvesting strategies on the population dynamics of tropical trees.

Several forest plant species are harvested both lethally for their timber and non-lethally for their non-timber forest products by the local people for cultural and economic reasons. To maximize yield, harvesters target various life stages of these species including both adults and juveniles particularly when the number of harvestable adults decline. The demographic consequences of harvesting various plant sizes differ based on what life stage is targeted. In this paper, we develop a size-structured, seasonal system of difference equations and corresponding matrix model with time-varying harvest to model the effects of size-dependent harvesting strategies on the population dynamics of tropical trees. We illustrate numerically our work specifically on African mahogany, Khaya senegalensis, a tropical tree in Benin. Novel applications and combinations of previously established matrix compression algorithms are presented to determine certain rates in our model, with other rates coming from the use of generalized linear modeling and ordinary least squares estimation incorporating observed population data. Harvesting rates for two types of populations are estimated, one with simulated harvest and the other experiencing natural harvest. Eigenvalue analysis suggests that for the populations in our study, harvesting may not have a drastic effect on the long-term persistence of the population. However, this should be taken with caution given that our model does not account for stochastic environmental variations that can interactively reduce population growth rates.

Optimal anti-amyloid-beta therapy for Alzheimer's disease via a personalized mathematical model.

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.

Geographic disparities and determinants of COVID-19 incidence risk in the greater St. Louis Area, Missouri (United States).

BACKGROUND: Evidence seems to suggest that the risk of Coronavirus Disease 2019 (COVID-19) might vary across communities due to differences in population characteristics and movement patterns. However, little is known about these differences in the greater St Louis Area of Missouri and yet this information is useful for targeting control efforts. Therefore, the objectives of this study were to investigate (a) geographic disparities of COVID-19 risk and (b) associations between COVID-19 risk and socioeconomic, demographic, movement and chronic disease factors in the Greater St. Louis Area of Missouri, USA. METHODS: Data on COVID-19 incidence and chronic disease hospitalizations were obtained from the Department of Health and Missouri Hospital Association, respectively. Socioeconomic and demographic data were obtained from the 2018 American Community Survey while population mobility data were obtained from the SafeGraph website. Choropleth maps were used to identify geographic disparities of COVID-19 risk and several sociodemographic and chronic disease factors at the ZIP Code Tabulation Area (ZCTA) spatial scale. Global negative binomial and local geographically weighted negative binomial models were used to investigate associations between ZCTA-level COVID-19 risk and socioeconomic, demographic and chronic disease factors. RESULTS: There were geographic disparities found in COVID-19 risk. Risks tended to be higher in ZCTAs with high percentages of the population with a bachelor's degree (p<0.0001) and obesity hospitalizations (p<0.0001). Conversely, risks tended to be lower in ZCTAs with high percentages of the population working in agriculture (p<0.0001). However, the association between agricultural occupation and COVID-19 risk was modified by per capita between ZCTA visits. Areas that had both high per capita between ZCTA visits and high percentages of the population employed in agriculture had high COVID-19 risks. The strength of association between agricultural occupation and COVID-19 risk varied by geographic location. CONCLUSIONS: Geographic disparities of COVID-19 risk exist in the St. Louis area and are associated with sociodemographic factors, population movements, and obesity hospitalization risks. The latter is particularly concerning due to the growing prevalence of obesity and the known immunological impairments among obese individuals. Therefore, future studies need to focus on improving our understanding of the relationships between COVID-19 vaccination efficacy, obesity and waning of immunity among obese individuals so as to better guide vaccination regimens and reduce disparities.

A vaccination model for COVID-19 in Gauteng, South Africa.

The COVID-19 pandemic provides an opportunity to explore the impact of government mandates on movement restrictions and non-pharmaceutical interventions on a novel infection, and we investigate these strategies in early-stage outbreak dynamics. The rate of disease spread in South Africa varied over time as individuals changed behavior in response to the ongoing pandemic and to changing government policies. Using a system of ordinary differential equations, we model the outbreak in the province of Gauteng, assuming that several parameters vary over time. Analyzing data from the time period before vaccination gives the approximate dates of parameter changes, and those dates are linked to government policies. Unknown parameters are then estimated from available case data and used to assess the impact of each policy. Looking forward in time, possible scenarios give projections involving the implementation of two different vaccines at varying times. Our results quantify the impact of different government policies and demonstrate how vaccinations can alter infection spread.

Geographic disparities and predictors of COVID-19 hospitalization risks in the St. Louis Area, Missouri (USA).

BACKGROUND: There is evidence of geographic disparities in COVID-19 hospitalization risks that, if identified, could guide control efforts. Therefore, the objective of this study was to investigate Zip Code Tabulation Area (ZCTA)-level geographic disparities and identify predictors of COVID-19 hospitalization risks in the St. Louis area. METHODS: Hospitalization data for COVID-19 and several chronic diseases were obtained from the Missouri Hospital Association. ZCTA-level data on socioeconomic and demographic factors were obtained from the American Community Survey. Geographic disparities in distribution of COVID-19 age-adjusted hospitalization risks, socioeconomic and demographic factors as well as chronic disease risks were investigated using choropleth maps. Predictors of ZCTA-level COVID-19 hospitalization risks were investigated using global negative binomial and local geographically weighted negative binomial models. RESULTS: COVID-19 hospitalization risks were significantly higher in ZCTAs with high diabetes hospitalization risks (p < 0.0001), COVID-19 risks (p < 0.0001), black population (p = 0.0416), and populations with some college education (p = 0.0005). The associations between COVID-19 hospitalization risks and the first three predictors varied by geographic location. CONCLUSIONS: There is evidence of geographic disparities in COVID-19 hospitalization risks that are driven by differences in socioeconomic, demographic and health-related factors. The impacts of these factors vary by geographical location implying that a 'one-size-fits-all' approach may not be appropriate for management and control. Using both global and local models leads to a better understanding of geographic disparities. These findings are useful for informing health planning to identify geographic areas likely to have high numbers of individuals needing hospitalization as well as guiding vaccination efforts.

Mathematical modeling of the influence of cultural practices on cholera infections in Cameroon.

The Far North Region of Cameroon, a high risk cholera endemic region, has been experiencing serious and recurrent cholera outbreaks in recent years. Cholera outbreaks in this region are associated with cultural practices (traditional and religious beliefs). In this paper, we introduce a mathematical model of the influence of cultural practices on the dynamics of cholera in the Far North Region. Our model is an SEIR type model with a pathogen class and multiple susceptible classes based on traditional and religious beliefs. Using daily reported cholera cases from three health districts (Kaélé, Kar Hay and Moutourwa) in the Far North Region from June 25, 2019 to August 16, 2019, we estimate parameter values of our model and use Akaike information criterion (AIC) to demonstrate that our model gives a good fit for our data on cholera cases. We use sensitivity analysis to study the impact of each model parameter on the threshold parameter (control reproduction number), Rc, and the number of model predicted cholera cases. Finally, we investigate the effect of cultural practices on the number of cholera cases in the region.