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.

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 (³¹P MRS) outcome measures and evaluated their relationship with function in lower limb skeletal muscle of dysferlinopathy patients.Methods: Quantitative MRI/³¹P 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 ³¹P 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 ³¹P 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 ³¹P MRS indices were significantly different in patients as compared with controls (P < 0.006), except for pH_w, 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/³¹P 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.

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. 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. 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. 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.

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 ofBorrelia 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.

Researchers have observed that response of tumor cells to treatment varies depending on whether the cells are grown in monolayer, asin vitrospheroids orin vivo. This study uses data from the literature on monolayer treatment of SK-N-SH neuroblastoma cells with 15-deoxy-PGJ2and 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 ofin vitrotumor 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-PGJ2is 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.

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.