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.

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.

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.

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.

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.

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.].

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

Researchers have observed that response of tumor cells to treatment varies depending on whether the cells are grown in monolayer, as in vitro spheroids or in vivo. This study uses data from the literature on monolayer treatment of SK-N-SH neuroblastoma cells with 15-deoxy-PGJ2 and couples it with data on growth rates for untreated SK-N-SH neuroblastoma cells grown as multicellular spheroids. A linear model is constructed for untreated and treated monolayer data sets, which is tuned to growth, death, and cell cycle data for the monolayer case for both control and treatment with 15-deoxy-PGJ2. The monolayer model is extended to a five-dimensional nonlinear model of in vitro tumor spheroid growth and treatment that includes compartments of the cell cycle (G1, S, G2/M) as well as quiescent (Q) and necrotic (N) cells. Monolayer treatment data for 15-deoxy-PGJ2 is used to derive a prediction of spheroid response under similar treatments. For short periods of treatment, spheroid response is less pronounced than monolayer response. The simulations suggest that the difference in response to treatment of monolayer versus spheroid cultures observed in laboratory studies is a natural consequence of tumor spheroid physiology rather than any special resistance to treatment.

A comparison of five malaria transmission models: benchmark tests and implications for disease control.

BACKGROUND: Models for malaria transmission are usually compared based on the quantities tracked, the form taken by each term in the equations, and the qualitative properties of the systems at equilibrium. Here five models are compared in detail in order to develop a set of performance measures that further illuminate the differences among models. METHODS: Five models of malaria transmission are compared. Parameters are adjusted to correspond to similar biological quantities across models. Nine choices of parameter sets/initial conditions are tested for all five models. The relationship between malaria incidence in humans and (1) malaria incidence in vectors, (2) man-biting rate, and (3) entomological inoculation rate (EIR) at equilibrium is tested for all models. A sensitivity analysis for all models is conducted at all parameter sets. Overall sensitivities are ranked for each of the five models. A set of simple control interventions is tested on two of the models. RESULTS: Four of these models behave consistently over a set of nine choices of parameters and initial conditions, with one behaving significantly differently. Two of the models do not match reported entomological inoculation rate data well. The sensitivity profiles, although consistently having similar top parameters, vary not only between models but among choices of parameters and initial conditions. A numerical experiment on two of the models illustrates the effect of these differences on control strategies, showing significant differences between models in predicting which of the control measures are more effective. CONCLUSIONS: A set of benchmark tests based on performance measures are developed to be used on any proposed malaria transmission model to test its overall behaviour in comparison to both other models and data sets.

Formalizing an integrative, multidisciplinary cancer therapy discovery workflow.

Although many clinicians and researchers work to understand cancer, there has been limited success to effectively combine forces and collaborate over time, distance, data, and budget constraints. Here we present a workflow template for multidisciplinary cancer therapy that was developed during the 2nd Annual Workshop on Cancer Systems Biology sponsored by Tufts University, Boston, Massachusetts, in July 2012. The template was applied to the development of a metronomic therapy backbone for neuroblastoma. Three primary groups were identified: clinicians, biologists, and quantitative scientists (mathematicians, computer scientists, and engineers). The workflow described their integrative interactions; parallel or sequential processes; data sources and computational tools at different stages as well as the iterative nature of therapeutic development from clinical observations to in vitro, in vivo, and clinical trials. We found that theoreticians in dialog with experimentalists could develop calibrated and parameterized predictive models that inform and formalize sets of testable hypotheses, thus speeding up discovery and validation while reducing laboratory resources and costs. The developed template outlines an interdisciplinary collaboration workflow designed to systematically investigate the mechanistic underpinnings of a new therapy and validate that therapy to advance development and clinical acceptance.

Properties of tumor spheroid growth exhibited by simple mathematical models.

Solid tumors, whether in vitro or in vivo, are not an undifferentiated mass of cells. They include necrotic regions, regions of cells that are in a quiescent state (either slowly growing or not growing at all), and regions where cells proliferate rapidly. The decision of a cell to become quiescent or proliferating is thought to depend on both nutrient and oxygen availability and on the presence of tumor necrosis factor, a substance produced by necrotic cells that somehow inhibits the further growth of the tumor. Several different models have been suggested for the basic growth rate of in vitro tumor spheroids, and several different mechanisms are possible by which tumor necrosis factor might halt growth. The models predict the trajectory of growth for a virtual tumor, including proportions of the various components during its time evolution. In this paper we look at a range of hypotheses about basic rates tumor growth and the role of tumor necrotic factor, and determine what possible tumor growth patterns follow from each of twenty-five reasonable models. Proliferating, quiescent and necrotic cells are included, along with tumor necrosis factor as a potential inhibitor of growth in the proliferating pool and two way exchange between the quiescent and proliferating pools. We show that a range of observed qualitative properties of in vitro tumor spheroids at equilibrium are exhibited by one particular simple mathematical model, and discuss implications of this model for tumor growth.