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Abstract The use of antimicrobial drugs in food-producing animals contributes to 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 dynamics 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-FDA-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 non-FDA-approved scenario (7.5 mg/kg, two doses 24 h 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 those that decrease resistant E. coli the most, suggesting a trade-off between both outcomes. The sensitivity analysis suggests that bacterial populations were the most sensitive to drug conversion factors into plasma ( $${\beta}$$ β ), elimination of the drug from the colon ( $$\vartheta$$ ϑ ), fifty percent sensitive bacteria (P. multocida) killing effect ( $${\text{L}}_{\text{s50}}$$ L s50 ), fifty percent of bacteria (E. coli) above ECOFF killing effect ( $${\text{C}}_{\text{r50}}$$ C r50 ), and net drug transfer rate in the lung ( $$\gamma$$ γ ) parameters.

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.

BackgroundLimited 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.MethodsThe 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.ResultsCounties 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.ConclusionThe 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.

Healthcare-associated infections (HAI), particularly those involving multi-drug resistant organisms (MDRO), pose a significant public health threat. Understanding the transmission of these pathogens in short-term acute care hospitals (STACH) is crucial for effective control. Mathematical and computational models play a key role in studying transmission but often overlook the influence of long-term care facilities (LTCFs) and the broader community on transmission. In a systematic scoping review of 4,733 unique studies from 2016 to 2022, we explored the modeling landscape of the hospital-community interface in HAI-causing pathogen transmission. Among the 29 eligible studies, 28 % (n = 8) exclusively modeled LTCFs, 45 % (n = 13) focused on non-healthcare-related community settings, and 31 % (n = 9) considered both settings. Studies emphasizing screening and contact precautions were more likely to include LTCFs but tended to neglect the wider community. This review emphasizes the crucial need for comprehensive modeling that incorporates the community's impact on both clinical and public health outcomes.

ABSTRACTThe 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.

Abstract Managing social‐ecological systems (SES) requires balancing the need to tailor actions to local heterogeneity and the need to work over large areas to accommodate the extent of SES. This balance is particularly challenging for policy since the level of government where the policy is being developed determines the extent and resolution of action. We make the case for a new research agenda focused on ecological federalism that seeks to address this challenge by capitalizing on the flexibility afforded by a federalist system of governance. Ecological federalism synthesizes the environmental federalism literature from law and economics with relevant ecological and biological literature to address a fundamental question: What aspects of SES should be managed by federal governments and which should be allocated to decentralized state governments? This new research agenda considers the bio‐geo‐physical processes that characterize state‐federal management tradeoffs for biodiversity conservation, resource management, infectious disease prevention, and invasive species control. Read the free Plain Language Summary for this article on the Journal blog.

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.

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.

Abstract Adelges tsugae Annand, the hemlock woolly adelgid, is an invasive insect pest of Tsuga canadensis (L.) Carriere, eastern hemlock, in the eastern United States. An A. tsugae infestation often results in the death of T. canadensis within years and has caused significant changes to hemlock forests. Cycles in T. canadensis health and A. tsugae densities seem to be an important feature in A. tsugae population 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 in T. canadensis health and A. tsugae density. We use field data from Virginia to develop the model and to perform parameter estimation. The mechanisms we represent in the model include an A. tsugae density‐dependent T. canadensis growth rate, a T. canadensis health‐dependent A. tsugae mortality rate, and a density‐dependent A. tsugae mortality rate, which produce cycles in T. canadensis health and A. tsugae density commonly seen with the A. tsugae system in the eastern United States. We test sets of initial conditions to determine the scenarios that will likely lead to T. canadensis mortality and explore longer term dynamics of the system. In general, low and high T. canadensis health initial condition values result in likely T. canadensis mortality while T. canadensis with medium health initial condition values are predicted to survive.

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.

IntroductionRunners 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.MethodsWe 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.ResultsAs 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.DiscussionOur 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.

Abstract 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

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. Author summary Hormonal contraceptives composed of exogenous estrogen and/or progesterone are commonly administered artificial means of birth control. Despite many benefits, adverse side effects associated with high doses such as thrombosis and myocardial infarction, cause hesitation to usage. Our study presents an improved mathematical model for hormonal control of the menstrual cycle and applies optimal control theory to minimize total exogenous estrogen and/or progesterone dose, and determine timing of administration that lead to contraception. We observe a reduction in dosage of about 92% in estrogen monotherapy and 43% in progesterone monotherapy. Our simulations show that it is most effective to deliver the estrogen contraceptive in the mid follicular phase. In addition, we illustrate that combination therapy significantly lower doses further. Our findings may give clinicians insights into optimal dosing scheme for contraception.

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-jurisdiction SIRS model 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.

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), $ \mathcal{R}_c $, 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.

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.

Abstract 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.

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 (pConclusions 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.

In Appalachia, La Crosse virus (LACV) is a leading pediatric arbovirus and public health concern for children under 16 years. LACV is transmitted via the bite of an infected Aedes mosquito. Thus, it is imperative to understand the dynamics of the local vector population in order to assess risk and transmission. Using entomological data collected from Knox County, Tennessee in 2013, we formulate an environmentally-driven system of ordinary differential equations to model mosquito population dynamics over a single season. Further, we include infected compartments to represent LACV transmission within the mosquito population. Findings suggest that the model, with dependence on degree days and accumulated precipitation, can closely describe field data. This model confirms the need to include these environmental variables when planning control strategies.

La Crosse Virus (LACV) is an arbovirus found in Eastern Appalachia and can cause pediatric encephalitis in prepubescent children. To assess the risk and transmission of this disease, it is particularly important to understand the average population of Aedes mosquitoes, which are the vectors of this virus. We use a deterministic compartmental model to study the effects of environmental factors on the population dynamics of Aedes mosquitoes in the Knox County area. We use locally-collected mosquito population data to adjust our model outputs and find that model transitions are heavily dependent on the fluctuations of both temperature and accumulated precipitation. These findings should be considered for mosquito management in Southern Appalachia, as well as in other regions with slight modifications to our model.

Public involvement in Ebola Virus Disease (EVD) prevention efforts is key to reducing disease outbreaks. Targeted education through practical health information to particular groups and sub-populations is crucial to controlling the disease. In this paper, we study the dynamics of Ebola virus disease in the presence of public health education with the aim of assessing the role of behavior change induced by health education to the dynamics of an outbreak. The power of behavior change is evident in two outbreaks of EVD that took place in Sudan only 3 years apart. The first occurrence was the first documented outbreak of EVD and produced a significant number of infections. The second outbreak produced far fewer cases, presumably because the population in the region learned from the first outbreak. We derive a system of ordinary differential equations to model these two contrasting behaviors. Since the population in Sudan learned from the first outbreak of EVD and changed their behavior prior to the second outbreak, we use data from these two instances of EVD to estimate parameters relevant to two contrasting behaviors. We then simulate a future outbreak of EVD in Sudan using our model that contains two susceptible populations, one being more informed about EVD. Our finding show how a more educated population results in fewer cases of EVD and highlights the importance of ongoing public health education. Keywords: Ebola virus disease, Public health education, Outbreaks, Mathematical model, Simulations, Infectious disease model

The 2014–2016 West African outbreak of Ebola Virus Disease (EVD) was the largest and most deadly to date. Contact tracing, following up those who may have been infected through contact with an infected individual to prevent secondary spread, plays a vital role in controlling such outbreaks. Our aim in this work was to mechanistically represent the contact tracing process to illustrate potential areas of improvement in managing contact tracing efforts. We also explored the role contact tracing played in eventually ending the outbreak. We present a system of ordinary differential equations to model contact tracing in Sierra Leonne during the outbreak. Using data on cumulative cases and deaths, we estimate most of the parameters in our model. We include the novel features of counting the total number of people being traced and tying this directly to the number of tracers doing this work. Our work highlights the importance of incorporating changing behavior into one’s model as needed when indicated by the data and reported trends. Our results show that a larger contact tracing program would have reduced the death toll of the outbreak. Counting the total number of people being traced and including changes in behavior in our model led to better understanding of disease management.

We formulate and then analyze a multi-group coupled within-host model of ODEs and between-host model of ODE and first-order PDEs, using the Human Immunodeficiency Virus (HIV) for illustration. The basic reproduction number of the multi-group coupled epidemiological model is derived, steady states solutions are calculated and stability analysis of equilbria is investigated. An optimal control problem for our model with drug treatment on the multi-group within-host system is formulated and analyzed. Ekeland's principle is used in proving existence and uniqueness of an optimal control pair. Numerical simulations based on the semi-implicit finite difference schemes and the forward-backward sweep iterative method are obtained.

The role of spatial arrangements on the spread and management strategies of a cholera epidemic is investigated. We consider the effect of human and pathogen movement on optimal vaccination strategies. A metapopulation model is used, incorporating a susceptible–infected–recovered system of differential equations coupled with an equation modelling the concentration of Vibrio cholerae in an aquatic reservoir. The model compared spatial arrangements and varying scenarios to draw conclusions on how to effectively manage outbreaks. The work is motivated by the 2010 cholera outbreak in Haiti. Results give guidance for vaccination strategies in response to an outbreak.

Canine distemper virus (CDV) is a highly contagious virus that can cause outbreaks, specifically in crowding situations, such as an animal shelter, in which a large number of susceptible dogs are brought together. Introduction of this virus into a shelter can have devastating effects, potentially resulting in shelter canine depopulation. Motivated by recent outbreaks in Tennessee, a mathematical model was constructed to find relevant factors that could assist in preventing or reducing outbreaks. A system of ordinary differential equations was derived to represent the spread of CDV through susceptible, exposed, infected and recovered (S–E–I–R) classes as well as a vaccinated (V) class. Our model was adapted to represent a local Knoxville shelter. The effects of various control methods, both preventative and corrective, on disease spread were investigated.

An SIR type model is expanded to include the use of education or information given to the public as a control to manage a disease outbreak when effective treatments or vaccines are not readily available or too costly to be widely used. The information causes a change in behavior resulting in three susceptible classes. We study stability analysis and use optimal control theory on the system of differential equations to achieve the goal of minimizing the infected population (while minimizing the cost). We illustrate our results with some numerical simulations.

Managing invasive species in rivers can be assisted by appropriate adjustment of flow rates. Using a partial differential equation (PDE) model representing an invasive population in a river, we investigate controlling the water discharge rate as a management strategy. Our goal is to see how controlling the water discharge rate will affect the invasive population, and more specifically how water discharges may force the invasive population downstream. We complete the analysis of a flow control problem, which seeks to minimize the invasive population upstream while minimizing the cost of this management. Using an optimality system, consisting of our population PDE, an adjoint PDE, and corresponding optimal control characterization, we illustrate some numerical simulations in which parameters are varied to determine how far upstream the invasive population reaches. We also change the river’s cross-sectional area to investigate its impact on the optimal control.

We consider an optimal fishery harvesting problem using an age-structured population model with nonlinear recruitment. The motivating example is Atlantic Cod. The goal is to maximize the profit (total gain) of fishing. We seek to find the optimal harvesting strategy for each age class, but also to find the optimal net size. Using the extension of Pontryagin’s Maximum Principle to discrete systems, we are able to derive the necessary conditions and the characterizations for the optimal harvesting strategies. Numerical simulations for both Beverton-Holt and Ricker recruitment functions are provided.

We consider a bilinear optimal control problem with the state equation being a Kirchhoff plate equation. The control is a function of the spatial variables and acts as a multiplier of the velocity term. The unique optimal control, driving the state solution close to a desired evolution function, is characterized in terms of the solution of the optimality system.

We examine an ordinary differential system modeling the interaction of the HIV virus and the immune system of the human body. The optimal control represents a percentage effect the chemotherapy has on the interaction of the CD4$^+$T cells with the virus. We maximize the benefit based on the T cell count and minimize the systemic cost based on the percentage of chemotherapy given. Existence of an optimal control is proven, and the optimal control is uniquely characterized in terms of the solution of the optimality system, which is the state system coupled with the adjoint system. In addition, numerical examples are given for illustration.

Combination antiviral drug therapy improves the survival rates of patients chronically infected with hepatitis B virus by controlling viral replication and enhancing immune responses. Some of these drugs have side effects that make them unsuitable for long-term administration. To address the trade-off between the positive and negative effects of the combination therapy, we investigated an optimal control problem for a delay differential equation model of immune responses to hepatitis virus B infection. Our optimal control problem investigates the interplay between virological and immunomodulatory effects of therapy, the control of viremia and the administration of the minimal dosage over a short period of time. Our numerical results show that the high drug levels that induce immune modulation rather than suppression of virological factors are essential for the clearance of hepatitis B virus.