To explore pesticide uptake from soil into a growing potato, a moving-boundary dynamic model is proposed on the basis of the radical diffusion process of a chemical to a sphere. This model, which considers the logistic growth of the potato tuber, describes two hypothetical processes of chemical diffusion within a growing tuber. The model was tested in an illustrative case study for an application of chlorpyrifos. Results indicate that the distribution of chlorpyrifos concentrations along the potato radius is significantly affected by the tuber development. In comparison of our results to results from a classic model using a fixed boundary, the proposed dynamic model yields a quick and big jump for both the average concentration and bioconcentration factor (BCF) of chlorpyrifos in the potato as a result of the sigmoid expansion boundary. Overall, the dynamic model predicts that chlorpyrifos BCFs in the potato at harvest are higher than those using the classical model. In comparison of model results to measured uptake of chlorpyrifos into potato at harvest, the dynamic model shows better performance than the classical model. Our results provide a new perspective on pesticide uptake into potatoes and inform human health risk assessment for pesticides applied at different tuber growth stages.

In this paper, we proposed a coupled Patlak-Keller-Segel-Navier-Stokes system, which has dissipative free energy. On the plane R 2 , we proved that if the total mass of the cells is strictly less than 8π, then classical solutions exist for any finite time and their H s -Sobolev norms are almost uniformly bounded in time. On the torus T 2 , we proved that under the 8π subcritical mass constraint, the solutions are uniformly bounded in time.

Approximately 1 in 200 infants is born with congenital cytomegalovirus (CMV), making it the most common congenital infection. About 1 in 5 congenitally-infected babies will suffer long-term sequelae, including sensorineural deafness, intellectual disability, and epilepsy. CMV infection is highly species-dependent, and the Rhesus CMV (RhCMV) infection of rhesus monkey fetuses is the only animal model that replicates essential features of congenital CMV infection in humans, including placental transmission, fetal disease, and fetal loss. To better understand the determinants and dynamics of congenital CMV transmission, we developed a mathematical model for placental transmission, comprising of maternal, placental, and fetal compartments using parameters from literature and experimental data from RhCMV seronegative rhesus macaques inoculated with RhCMV at 7.7-9.0 weeks of pregnancy. The model was then used to study the effect of the timing of inoculation, maternal immune suppression, and hyper-immune globulin infusion on the risk of placental transmission in the context of primary and reactivated chronic maternal CMV infection.

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