Global Analysis of a piecewise smooth epidemiological model of COVID-19.

Despite the huge relevance of vaccines for preventing COVID-19, physical isolation and quarantine of infected individuals are still the key strategies to fight against the COVID-19 pandemic. Based on a COVID-19 transmission epidemiological model governed by ordinary differential equations, here we propose an intermittent non-pharmacological protocol to control the fraction of infected individuals. In our approach, unlike what generically happens for numerical simulation models, we provide a global analysis of the model, giving qualitative information about every initial condition. Under some simple hypothesis and variations of parameters, we present some bifurcations and we are able to predict the minimum social distancing effort that do not collapse the health system.

Maternal Passive Immunity and Dengue Hemorrhagic Fever in Infants.

Dengue hemorrhagic fever (DHF) can occur in primary dengue virus infection of infants [Formula: see text] year of age. To understand the presumed role of maternal dengue-specific antibodies received until birth in the development of this primary DHF in infants, we investigated a mathematical model based on a system of nonlinear ordinary differential equations that mimics cells, virus and antibodies interactions. The neutralization and enhancement activities of maternal antibodies against the virus are represented by a function derived from experimental data and knowledge from the medical literature. The analytic study of the model shows the existence of two equilibriums, a disease-free equilibrium and an endemic one. We performed the asymptotic stability analysis for these two equilibriums. The local asymptotic stability of the endemic equilibrium (DHF equilibrium) corresponds to the occurrence of DHF. Numerical results are also presented in order to illustrate the mathematical analysis performed, highlighting the most important parameters that drive model dynamics. We defined the age at which DHF occurs as the time when the infection takes off that means at the inflection point of the curve of infected cell population. We showed that this age corresponds to the one at which maximum enhancing activity for dengue infection appears. This critical time for the occurrence of DHF is calculated from the model to be approximately 2 months after the time for maternal dengue neutralizing antibodies to degrade below a protective level, which corresponds to what is observed in the experimental data from the literature.

Multichannel AC Biosusceptometry System to Map Biodistribution and Assess the Pharmacokinetic Profile of Magnetic Nanoparticles by Imaging.

In this paper, the application of a technique to evaluate in vivo biodistribution of magnetic nanoparticles (MNP) is addressed: the Multichannel AC Biosusceptometry System (MC-ACB). It allows real-time assessment of magnetic nanoparticles in both bloodstream clearance and liver accumulation, where a complex network of inter-related cells is responsible for MNP uptake. Based on the acquired MC-ACB images, we propose a mathematical model which helps to understand the distribution and accumulation pharmacokinetics of MNP. The MC-ACB showed a high time resolution to detect and monitor MNP, providing sequential images over the particle biodistribution. Utilizing the MC-ACB instrument, we assessed regions corresponding to the heart and liver, and we determined the MNP transfer rates between the bloodstream and the liver. The pharmacokinetic model resulted in having a strong correlation with the experimental data, suggesting that the MC-ACB is a valuable and accessible imaging device to assess in vivo and real-time pharmacokinetic features of MNP.