Optimal control of a tick population with a view to control of Rocky Mountain Spotted Fever.

In some regions of the Americas, domestic dogs are the host for the tick vector Rhipicephalus sanguineus, and spread the tick-borne pathogen Rickettsia rickettsii, which causes Rocky Mountain Spotted Fever (RMSF) in humans. Interventions are carried out against the vector via dog collars and acaricidal wall treatments. This paper investigates the optimal control of acaricidal wall treatments, using a prior model for populations and disease transmission developed for this particular vector, host, and pathogen. It is modified with a death term during questing stages reflecting the cost of control and level of coverage. In the presence of the control, the percentage of dogs and ticks infected with Ri. rickettsii decreases in a short period and remains suppressed for a longer period, including after treatment is discontinued. Risk of RMSF infection declines by 90% during this time. In the absence of re-application, infected tick and dog populations rebound, indicating the eventual need for repeated treatment.

A simulation of parental and glycolytic tumor phenotype competition predicts observed responses to pH changes and increased glycolysis after anti-VEGF therapy.

Clinical cancers are typically spatially and temporally heterogeneous, containing multiple microenvironmental habitats and diverse phenotypes and/or genotypes, which can interact through resource competition and direct or indirect interference. A common intratumoral evolutionary pathway, probably initiated as adaptation to hypoxia, leads to the "Warburg phenotype" which maintains high glycolytic rates and acid production, even in normoxic conditions. Since individual cancer cells are the unit of Darwinian selection, intraspecific competition dominates intratumoral evolution. Thus, elements of the Warburg phenotype become key "strategies" in competition with cancer cell populations that retain the metabolism of the parental normal cells. Here we model the complex interactions of cell populations with Warburg and parental phenotypes as they compete for access to vasculature, while subject to direct interference by Warburg-related acidosis. In this competitive environment, vasculature delivers nutrients, removes acid and necrotic detritus, and responds to signaling molecules (VEGF and TNF-α). The model is built in a nested fashion and growth parameters are derived from monolayer, spheroid, and xenograft experiments on prostate cancer. The resulting model of in vivo tumor growth reaches a steady state, displaying linear growth and coexistence of both glycolytic and parental phenotypes consistent with experimental observations. The model predicts that increasing tumor pH sufficiently early can arrest the development of the glycolytic phenotype, while decreasing tumor pH accelerates this evolution and increases VEGF production. The model's predicted dual effects of VEGF blockers in decreasing tumor growth while increasing the glycolytic fraction of tumor cells has potential implications for optimizing angiogenic inhibitors.

Temperature-dependent population dynamics for Aedes aegypti in outdoor, indoor, and enclosed habitats: a mathematical model for five North American cities.

A model for the Aedes aegypti lifecycle is developed that takes into account temperature-dependent maturation and death rates for several life stages, wet and dry egg oviposition with flooding, as well as three classes of larval habitat with different temperature profiles: outdoor (subject to external temperature fluctuations, human-inhabited), indoor (temperature moderated, human-inhabited, interior), and enclosed (temperature moderated, human free, exterior). An equilibrium analysis shows that the temperature range of outdoor viable equilibrium populations aligns closely with reported risk levels. Temperature patterns for El Paso, Texas; New York, New York; New Orleans, Louisiana; Orlando, Florida; and Miami, Florida, are considered. In four of these locations (all but New York), enclosed habitats can support mosquito populations even if all outdoor and indoor habitats are removed. In two locations (El Paso and New York) the model shows that in spite of the disappearance of adult mosquitoes during colder temperatures, populations reach seasonal steady state due to the survival of eggs. The results have implications for both vector and disease control.

Three-year quantitative magnetic resonance imaging and phosphorus magnetic resonance spectroscopy study in lower limb muscle in dysferlinopathy.

BACKGROUND: Natural history studies in neuromuscular disorders are vital to understand the disease evolution and to find sensitive outcome measures. We performed a longitudinal assessment of quantitative magnetic resonance imaging (MRI) and phosphorus magnetic resonance spectroscopy (31 P MRS) outcome measures and evaluated their relationship with function in lower limb skeletal muscle of dysferlinopathy patients. METHODS: Quantitative MRI/31 P MRS data were obtained at 3 T in two different sites in 54 patients and 12 controls, at baseline, and three annual follow-up visits. Fat fraction (FF), contractile cross-sectional area (cCSA), and muscle water T2 in both global leg and thigh segments and individual muscles and 31 P MRS indices in the anterior leg compartment were assessed. Analysis included comparisons between patients and controls, assessments of annual changes using a linear mixed model, standardized response means (SRM), and correlations between MRI and 31 P MRS markers and functional markers. RESULTS: Posterior muscles in thigh and leg showed the highest FF values. FF at baseline was highly heterogeneous across patients. In ambulant patients, median annual increases in global thigh and leg segment FF values were 4.1% and 3.0%, respectively (P < 0.001). After 3 years, global thigh and leg FF increases were 9.6% and 8.4%, respectively (P < 0.001). SRM values for global thigh FF were over 0.8 for all years. Vastus lateralis muscle showed the highest SRM values across all time points. cCSA decreased significantly after 3 years with median values of 11.0% and 12.8% in global thigh and global leg, respectively (P < 0.001). Water T2 values in ambulant patients were significantly increased, as compared with control values (P < 0.001). The highest water T2 values were found in the anterior part of thigh and leg. Almost all 31 P MRS indices were significantly different in patients as compared with controls (P < 0.006), except for pHw , and remained, similar as to water T2 , abnormal for the whole study duration. Global thigh water T2 at baseline was significantly correlated to the change in FF after 3 years (ρ = 0.52, P < 0.001). There was also a significant relationship between the change in functional score and change in FF after 3 years in ambulant patients (ρ = -0.55, P = 0.010). CONCLUSIONS: This multi-centre study has shown that quantitative MRI/31 P MRS measurements in a heterogeneous group of dysferlinopathy patients can measure significant changes over the course of 3 years. These data can be used as reference values in view of future clinical trials in dysferlinopathy or comparisons with quantitative MRI/S data obtained in other limb-girdle muscular dystrophy subtypes.

Modeling of Control Efforts against Rhipicephalus sanguineus, the Vector of Rocky Mountain Spotted Fever in Sonora Mexico.

Rocky Mountain spotted fever (RMSF) is a significant health problem in Sonora, Mexico. The tick vector, Rhipicephalus sanguineus, feeds almost exclusively on domestic dogs that, in this region, also serve as the reservoir for the tick-borne pathogen, Rickettsia rickettsii. A process-based mathematical model of the life cycle of R. sanguineus was developed to predict combinations of insecticidal dog collars and long-lasting insecticidal wall treatments resulting in suppression of indoor tick populations. Because of a high burden of RMSF in a rural community near the Sonora state capital of Hermosillo, a test area was treated with a combination of insecticidal dog collars and long-lasting insecticidal wall treatments from March 2018 to April 2019, with subsequent reduction in RMSF cases and deaths. An estimated 80% of the dogs in the area had collars applied and 15% of the houses were treated. Data on tick abundance on walls and dogs, collected during this intervention, were used to parameterize the model. Model results show a variety of treatment combinations likely to be as successful as the one carried out in the test community.

Larval flushing alters malaria endemicity patterns in regions with similar habitat abundance.

A model of Anopheles gambiae populations dynamics coupled with Plasmodium falciparum transmission dynamics is extended to include mechanisms of larval flushing which are known to occur. Flushing dynamics are modeled using a simulation that incorporates seasonal, autocorrelated, and random components based on 30 years of rainfall data for the Kakamega District of the western Kenya highlands. The model demonstrates that flushing phenomena can account for differences between regions with the same annual larval habitat pattern, changing the World Health Organization endemicity classification from either hyperendemic or holoendemic to hypoendemic disease patterns. Mesoendemic patterns of infection occur at the boundary of the holoendemic to hypoendemic transition. For some levels of flushing the entomological inoculation rate drops to an insignificant amount and disease disappears, while the annual indoor resting density remains well above zero. In these scenarios, the disease is hypoendemic, yet the model shows that outbreaks can occur when disease is introduced at particular time points.

Predicting Long-Term Asbestos Prevalence in Human Lungs, Lymph Nodes, and Remote Organs from Short-Term Murine Experiments.

Inhalation of asbestos fibers leads to a suite of fatal diseases that can manifest years, if not decades, after cessation of exposure. The first phase of disease progression occurs as fibers are transported from point of entry in the lungs throughout the entire body. A mathematical model is developed for the disposition of non-chrysotile asbestos in the body and, except for exposure levels, is parameterized by published data on short-term rat experiments. Asbestos exposure in individual humans is determined by matching published long-term lung data for nine patients. The resulting model predicts transport of fibers within the lymphatic system and prevalence of fibers in lymph nodes for these patients with reasonable accuracy. Model predictions for remote organs are compared against published observations. The model consists of a system of globally stable differential equations, and a sensitivity analysis was conducted. The model indicates that fiber density in lymph nodes is correlated with total exposure, level times duration, no matter whether there is a long-term, low-level exposure or short-term, high-level exposure. The model predicts that levels of sequestered asbestos reach steady state within five years of cessation of exposure, a timeline previously not known. The model suggests that the time to steady state is short compared to onset of disease, and that delayed onset of related disease may be a function of chemical and biological processes not in this model.

Dilution and amplification effects in Lyme disease: Modeling the effects of reservoir-incompetent hosts on Borrelia burgdorferi sensu stricto transmission.

The literature on Lyme disease includes a lively debate about the paradoxical role of changing deer populations. A decrease in the number of deer will both (1) reduce the incidence of Lyme disease by decreasing the host populations for ticks and therefore tick populations, and (2) enhance the incidence of Lyme disease by offering fewer reservoir-incompetent hosts for ticks, forcing the vector to choose reservoir-competent, and therefore possibly diseased, hosts to feed on. A review of field studies exploring the net impact of changing deer populations shows mixed results. In this manuscript, we investigate the hypothesis that the balance of these two responses to changing deer populations depends on the relative population sizes of reservoir-competent vs. reservoir-incompetent hosts and the presence of host preference in larval and adult stages. A temperature driven seasonal model of Borrelia burgdorferi sensu stricto (cause of Lyme disease) transmission among three host types (reservoir-competent infected and uninfected hosts, and reservoir-incompetent hosts) is constructed as a system of nonlinear ordinary differential equations. The model, which produces biologically reasonable results for both the tick vector Ixodes scapularis Say 1921 and the hosts, is used to investigate the effects of reservoir-incompetent host removal on both tick populations and disease prevalence for various relative population sizes of reservoir-competent hosts vs. reservoir-incompetent hosts. In summary, the simulation results show that the model with host preference appears to be more accurate than the one with no host preference. Given these results, we found that removal of adult I. scapularis(Say) hosts is likely to reduce questing nymph populations. At very low levels questing adult abundance may rise with lack of adult hosts. There is a dilution effect at low reservoir-competent host populations and there is an amplification effect at high reservoir-competent host populations.

Predicting the results of competition between two breast cancer lines grown in 3-D spheroid culture.

This study develops a novel model of a consumer-resource system with mobility included, in order to explain a novel experiment of competition between two breast cancer cell lines grown in 3D in vitro spheroid culture. The model reproduces observed differences in monoculture, such as overshoot phenomena and final size. It also explains both theoretically and through simulation the inevitable triumph of the same cell line in co-culture, independent of initial conditions. The mobility of one cell line (MDA-MB-231) is required to explain both the success and the rapidity with which that species dominates the population and drives the other species (MCF-7) to extinction. It is shown that mobility directly interferes with the other species and that the cost of that mobility is in resource usage rate.

Modeling the Sensitivity of Blacklegged Ticks (Ixodes scapularis) to Temperature and Land Cover in the Northeastern United States.

The prevalence of Lyme disease and other tick-borne diseases is dramatically increasing across the United States. While the rapid rise in Lyme disease is clear, the causes of it are not. Modeling Ixodes scapularis Say (Acari: Ixodidae), the primary Lyme disease vector in the eastern United States, presents an opportunity to disentangle the drivers of increasing Lyme disease, including climate, land cover, and host populations. We improved upon a recently developed compartment model of ordinary differential equations that simulates I. scapularis growth, abundance, and infection with Borrelia burgdorferi (Spirochaetales: Spirochaetaceae) by adding land cover effects on host populations, refining the representation of growth stages, and evaluating output against observed data. We then applied this model to analyze the sensitivity of simulated I. scapularis dynamics across temperature and land cover in the northeastern United States. Specifically, we ran an ensemble of 232 simulations with temperature from Hanover, New Hampshire and Storrs, Connecticut, and land cover from Hanover and Cardigan in New Hampshire, and Windsor and Danielson in Connecticut. Consistent with observations, simulations of I. scapularis abundance are sensitive to temperature, with the warmer Storrs climate significantly increasing the number of questing I. scapularis at all growth stages. While there is some variation in modeled populations of I. scapularis infected with B. burgdorferi among land cover distributions, our analysis of I. scapularis response to land cover is limited by a lack of observations describing host populations, the proportion of hosts competent to serve as B. burgdorferi reservoirs, and I. scapularis abundance.

A mathematical model of HIV dynamics treated with a population of gene-edited haematopoietic progenitor cells exhibiting threshold phenomenon.

The use of gene-editing technology has the potential to excise the CCR5 gene from haematopoietic progenitor cells, rendering their differentiated CD4-positive (CD4+) T cell descendants HIV resistant. In this manuscript, we describe the development of a mathematical model to mimic the therapeutic potential of gene editing of haematopoietic progenitor cells to produce a class of HIV-resistant CD4+ T cells. We define the requirements for the permanent suppression of viral infection using gene editing as a novel therapeutic approach. We develop non-linear ordinary differential equation models to replicate HIV production in an infected host, incorporating the most appropriate aspects found in the many existing clinical models of HIV infection, and extend this model to include compartments representing HIV-resistant immune cells. Through an analysis of model equilibria and stability and computation of $R_0$ for both treated and untreated infections, we show that the proposed therapy has the potential to suppress HIV infection indefinitely and return CD4+ T cell counts to normal levels. A computational study for this treatment shows the potential for a successful 'functional cure' of HIV. A sensitivity analysis illustrates the consistency of numerical results with theoretical results and highlights the parameters requiring better biological justification. Simulations of varying level production of HIV-resistant CD4+ T cells and varying immune enhancements as the result of these indicate a clear threshold response of the model and a range of treatment parameters resulting in a return to normal CD4+ T cell counts.

A Malaria Transmission Model Predicts Holoendemic, Hyperendemic, and Hypoendemic Transmission Patterns Under Varied Seasonal Vector Dynamics.

A model is developed of malaria (Plasmodium falciparum) transmission in vector (Anopheles gambiae) and human populations that include the capacity for both clinical and parasite suppressing immunity. This model is coupled with a population model for Anopheles gambiae that varies seasonal with temperature and larval habitat availability. At steady state, the model clearly distinguishes uns hypoendemic transmission patterns from stable hyperendemic and holoendemic patterns of transmission. The model further distinguishes hyperendemic from holoendemic disease based on seasonality of infection. For hyperendemic and holoendemic transmission, the model produces the relationship between entomological inoculation rate and disease prevalence observed in the field. It further produces expected rates of immunity and prevalence across all three endemic patterns. The model does not produce mesoendemic transmission patterns at steady state for any parameter choices, leading to the conclusion that mesoendemic patterns occur during transient states or as a result of factors not included in this study. The model shows that coupling the effect of varying larval habitat availability with the effects of clinical and parasite-suppressing immunity is enough to produce known patterns of malaria transmission.

Effect of Rising Temperature on Lyme Disease: Ixodes scapularis Population Dynamics and Borrelia burgdorferi Transmission and Prevalence.

Warmer temperatures are expected to increase the incidence of Lyme disease through enhanced tick maturation rates and a longer season of transmission. In addition, there could be an increased risk of disease export because of infected mobile hosts, usually birds. A temperature-driven seasonal model of Borrelia burgdorferi (Lyme disease) transmission among four host types is constructed as a system of nonlinear ordinary differential equations. The model is developed and parametrized based on a collection of lab and field studies. The model is shown to produce biologically reasonable results for both the tick vector (Ixodes scapularis) and the hosts when compared to a different set of studies. The model is used to predict the response of Lyme disease risk to a mean annual temperature increase, based on current temperature cycles in Hanover, NH. Many of the risk measures suggested by the literature are shown to change with increased mean annual temperature. The most straightforward measure of disease risk is the abundance of infected questing ticks, averaged over a year. Compared to this measure, which is difficult and resource-intensive to track in the field, all other risk measures considered underestimate the rise of risk with rise in mean annual temperature. The measure coming closest was "degree days above zero." Disease prevalence in ticks and hosts showed less increase with rising temperature. Single field measurements at the height of transmission season did not show much change at all with rising temperature.

Predictive Modeling of Neuroblastoma Growth Dynamics in Xenograft Model After Bevacizumab Anti-VEGF Therapy.

Neuroblastoma is the leading cause of cancer death in young children. Although treatment for neuroblastoma has improved, the 5-year survival rate of patients still remains less than half. Recent studies have indicated that bevacizumab, an anti-VEGF drug used in treatment of several other cancer types, may be effective for treating neuroblastoma as well. However, its effect on neuroblastoma has not been well characterized. While traditional experiments are costly and time-consuming, mathematical models are capable of simulating complex systems quickly and inexpensively. In this study, we present a model of vascular tumor growth of neuroblastoma IMR-32 that is complex enough to replicate experimental data across a range of tumor cell properties measured in a suite of in vitro and in vivo experiments. The model provides quantitative insight into tumor vasculature, predicting a linear relationship between vasculature and tumor volume. The tumor growth model was coupled with known pharmacokinetics and pharmacodynamics of the VEGF blocker bevacizumab to study its effect on neuroblastoma growth dynamics. The results of our model suggest that total administered bevacizumab concentration per week, as opposed to dosage regimen, is the major determining factor in tumor suppression. Our model also establishes an exponentially decreasing relationship between administered bevacizumab concentration and tumor growth rate.

Muscle MRI in patients with dysferlinopathy: pattern recognition and implications for clinical trials.

BACKGROUND AND OBJECTIVE: Dysferlinopathies are a group of muscle disorders caused by mutations in the DYSF gene. Previous muscle imaging studies describe a selective pattern of muscle involvement in smaller patient cohorts, but a large imaging study across the entire spectrum of the dysferlinopathies had not been performed and previous imaging findings were not correlated with functional tests. METHODS: We present cross-sectional T1-weighted muscle MRI data from 182 patients with genetically confirmed dysferlinopathies. We have analysed the pattern of muscles involved in the disease using hierarchical analysis and presented it as heatmaps. Results of the MRI scans have been correlated with relevant functional tests for each region of the body analysed. RESULTS: In 181 of the 182 patients scanned, we observed muscle pathology on T1-weighted images, with the gastrocnemius medialis and the soleus being the most commonly affected muscles. A similar pattern of involvement was identified in most patients regardless of their clinical presentation. Increased muscle pathology on MRI correlated positively with disease duration and functional impairment. CONCLUSIONS: The information generated by this study is of high diagnostic value and important for clinical trial development. We have been able to describe a pattern that can be considered as characteristic of dysferlinopathy. We have defined the natural history of the disease from a radiological point of view. These results enabled the identification of the most relevant regions of interest for quantitative MRI in longitudinal studies, such as clinical trials. CLINICAL TRIAL REGISTRATION: NCT01676077.

Reduction of Mosquito Abundance Via Indoor Wall Treatments: A Mathematical Model.

Insecticidal indoor residual wall treatment is a major tool for the control of malaria, with the goals of reducing indoor vector density and vector life span, in addition to reducing transmission rates of disease. Dynamics of the malaria vector, Anopheles gambiae, in the Emutete region in the Western Kenya highlands are based on an already existing model in the literature. In this paper, the framework is used to predict vector reduction due to four types of indoor wall treatments: two cases of indoor residual spraying of DDT and two types of pyrethrin-based INESFLY insecticidal paint. These treatments differ primarily in the duration of their persistence on walls. The model shows the extent of suppression of vector abundance over time due to each of the four treatments. It predicts that indoor residual spraying may have no noticeable effect at all if the percent coverage is not high enough or the persistence of the mortality effect is low, but will have a substantial effect at higher coverage rates and/or higher persistence. For treatments with longer persistence of mortality, the model predicts a coverage threshold above which extra treatment has little to no effect. For treatments of short persistence of mortality, the seasonal timing of treatment has a noticeable effect on the duration of vector suppression. Overall, the model supports claims in the literature that wall treatments have the capacity to reduce the vector burden.

A dynamical model of the transport of asbestos fibres in the human body.

We present a model for the transport of a single type of asbestos fibre through the human body. The model captures the transport modes that pertain particularly to the lungs and the mesothelium. Numerical solutions of the system follow observed movement in the body. We compare the accumulation of fibres in the lungs versus the mesothelium, and then we give analysis and results for various cases of exposure level and exposure time. Models, such as the one developed here, can give clues as to how asbestos fibres impact the body, and where to look for major impact.

Erratum to "A Model for Spheroid versus Monolayer Response of SK-N-SH Neuroblastoma Cells to Treatment with 15-Deoxy-PGJ2".

[This corrects the article DOI: 10.1155/2016/3628124.].

Left ventricular functional, structural and energetic effects of normal aging: Comparison with hypertension.

OBJECTIVES: Both aging and hypertension are significant risk factors for heart failure in the elderly. The purpose of this study was to determine how aging, with and without hypertension, affects left ventricular function. METHODS: Cross-sectional study of magnetic resonance imaging and 31P spectroscopy-based measurements of left ventricular structure, global function, strains, pulse wave velocity, high energy phosphate metabolism in 48 normal subjects and 40 treated hypertensive patients (though no other cardiovascular disease or diabetes) stratified into 3 age deciles from 50-79 years. RESULTS: Normal aging was associated with significant increases in systolic blood pressure, vascular stiffness, torsion, and impaired diastolic function (all P<0.05). Age-matched hypertension exacerbated the effects of aging on systolic pressure, and diastolic function. Hypertension alone, and not aging, was associated with increased left ventricular mass index, reduced energetic reserve, reduced longitudinal shortening and increased endocardial circumferential shortening (all P<0.05). Multiple linear regression analysis showed that these unique hypertensive features were significantly related to systolic blood pressure (P<0.05). CONCLUSIONS: 1) Hypertension adds to the age-related changes in systolic blood pressure and diastolic function; 2) hypertension is uniquely associated with changes in several aspects of left ventricular structure, function, systolic strains, and energetics; and 3) these uniquely hypertensive-associated parameters are related to the level of systolic blood pressure and so are potentially modifiable.

Modeling the population dynamics and community impacts of Ambystoma tigrinum: A case study of phenotype plasticity.

Phenotypic plasticity is the ability of an organism to change its phenotype in response to changes in the environment. General mathematical descriptions of the phenomenon rely on an abstract measure of "viability" that, in this study, is instantiated in the case of the Tiger Salamander, Ambystoma tigrinum. This organism has a point in its development when, upon maturing, it may take two very different forms. One is a terrestrial salamander (metamorph)that visits ponds to reproduce and eat, while the other is an aquatic form (paedomorph) that remains in the pond to breed and which consumes a variety of prey including its own offspring. A seven dimensional nonlinear system of ordinary differential equations is developed, incorporating small (Z) and large (B) invertebrates, Ambystoma young of the year (Y), juveniles (J), terrestrial metamorphs (A) and aquatic paedomorphs (P). One parameter in the model controls the proportion of juveniles maturing into A versus P. Solutions are shown to remain non-negative. Every effort was made to justify parameters biologically through studies reported in the literature. A sensitivity analysis and equilibrium analysis of model parameters demonstrate that morphological choice is critical to the overall composition of the Ambystoma population. Various population viability measures were used to select optimal percentages of juveniles maturing into metamorphs, with optimal choices differing considerably depending on the viability measure. The model suggests that the criteria for viability for this organism vary, both from location to location and also in time. Thus, optimal responses change with spatiotemporal variation, which is consistent with other phenotypically plastic systems. Two competing hypotheses for the conditions under which metamorphosis occurs are examined in light of the model and data from an Ambystoma tigrinum population at Mexican Cut, Colorado. The model clearly supports one of these over the other for this data set. There appears to be a mathematical basis to the general tenet of spatiotemporal variation being important for the maintenance of polyphenisms, and our results suggest that such variation may have cascading effects on population, community, and perhaps ecosystem dynamics because it drives the production of a keystone, cannibalistic predator.