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.

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.].

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.

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.