A probabilistic approach for the study of epidemiological dynamics of infectious diseases: Basic model and properties.

The dynamics of epidemiological phenomena associated to infectious diseases have long been modelled taking different approaches. However, recent pandemic events exposed many areas of opportunity to improve the existing models. We develop a stochastic model based on the idea that transitions between epidemiological stages are alike sampling processes that may involve more than one subset of the population or may be mostly dependent on time intervals defined by pathological or clinical criteria. We apply the model to simulate epidemics, analyse the final distribution of the case fatality ratio, and define a basic reproductive number to determine the existence of a probabilistic phase transition for the dynamics. The resulting modelling scheme is robust, easy to implement, and can readily lend itself for extensions aimed at answering questions that emerge from close examination of data trends, such as those emerging from the COVID-19 pandemic, and other infectious diseases.

Acute dopamine receptor blockade in substantia nigra pars reticulata: a possible model for drug-induced Parkinsonism.

Dopamine (DA) depletion modifies the firing pattern of neurons in the substantia nigra pars reticulata (SNr), shifting their mostly tonic firing toward irregularity and bursting, traits of pathological firing underlying rigidity and postural instability in Parkinson's disease (PD) patients and animal models of Parkinsonism (PS). Drug-induced Parkinsonism (DIP) represents 20-40% of clinical cases of PS, becoming a problem for differential diagnosis, and is still not well studied with physiological tools. It may co-occur with tardive dyskinesia. Here we use in vitro slice preparations including the SNr to observe drug-induced pathological firing by using drugs that most likely produce it, DA-receptor antagonists (SCH23390 plus sulpiride), to compare with firing patterns found in DA-depleted tissue. The hypothesis is that SNr firing would be similar under both conditions, a prerequisite to the proposal of a similar preparation to test other DIP-producing drugs. Firing was analyzed with three complementary metrics, showing similarities between DA depletion and acute DA-receptor blockade. Moreover, blockade of either nonselective cationic channels or Cav3 T-type calcium channels hyperpolarized the membrane and abolished bursting and irregular firing, silencing SNr neurons in both conditions. Therefore, currents generating firing in control conditions are in part responsible for pathological firing. Haloperidol, a DIP-producing drug, reproduced DA-receptor antagonist firing modifications. Since acute DA-receptor blockade induces SNr neuron firing similar to that found in the 6-hydroxydopamine model of PS, output basal ganglia neurons may play a role in generating DIP. Therefore, this study opens the way to test other DIP-producing drugs. NEW & NOTEWORTHY Dopamine (DA) depletion enhances substantia nigra pars reticulata (SNr) neuron bursting and irregular firing, hallmarks of Parkinsonism. Several drugs, including antipsychotics, antidepressants, and calcium channel antagonists, among others, produce drug-induced Parkinsonism. Here we show the first comparison between SNr neuron firing after DA depletion vs. firing found after acute blockade of DA receptors. It was found that firing in both conditions is similar, implying that pathological SNr neuron firing is also a physiological correlate of drug-induced Parkinsonism.

A thermodynamic description for physiological transmembrane transport.

A general formulation for both passive and active transmembrane transport is derived from basic thermodynamical principles. The derivation takes into account the energy required for the motion of molecules across membranes and includes the possibility of modeling asymmetric flow. Transmembrane currents can then be described by the general model in the case of electrogenic flow. As it is desirable in new models, it is possible to derive other well-known expressions for transmembrane currents as particular cases of the general formulation. For instance, the conductance-based formulation for current turns out to be a linear approximation of the general formula for current. Also, under suitable assumptions, other formulas for current based on electrodiffusion, like the constant field approximation by Goldman, can be recovered from the general formulation. The applicability of the general formulations is illustrated first with fits to existing data, and after, with models of transmembrane potential dynamics for pacemaking cardiocytes and neurons. The general formulations presented here provide a common ground for the biophysical study of physiological phenomena that depend on transmembrane transport.

Analysis of spatial mobility in subjects from a Dengue endemic urban locality in Morelos State, Mexico.

INTRODUCTION: Mathematical models and field data suggest that human mobility is an important driver for Dengue virus transmission. Nonetheless little is known on this matter due the lack of instruments for precise mobility quantification and study design difficulties. MATERIALS AND METHODS: We carried out a cohort-nested, case-control study with 126 individuals (42 cases, 42 intradomestic controls and 42 population controls) with the goal of describing human mobility patterns of recently Dengue virus-infected subjects, and comparing them with those of non-infected subjects living in an urban endemic locality. Mobility was quantified using a GPS-data logger registering waypoints at 60-second intervals for a minimum of 15 natural days. RESULTS: Although absolute displacement was highly biased towards the intradomestic and peridomestic areas, occasional displacements exceeding a 100-Km radius from the center of the studied locality were recorded for all three study groups and individual displacements were recorded traveling across six states from central Mexico. Additionally, cases had a larger number of visits out of the municipality´s administrative limits when compared to intradomestic controls (cases: 10.4 versus intradomestic controls: 2.9, p = 0.0282). We were able to identify extradomestic places within and out of the locality that were independently visited by apparently non-related infected subjects, consistent with houses, working and leisure places. CONCLUSIONS: Results of this study show that human mobility in a small urban setting exceeded that considered by local health authority's administrative limits, and was different between recently infected and non-infected subjects living in the same household. These observations provide important insights about the role that human mobility may have in Dengue virus transmission and persistence across endemic geographic areas that need to be taken into account when planning preventive and control measures. Finally, these results are a valuable reference when setting the parameters for future mathematical modeling studies.

Membranes with the same ion channel populations but different excitabilities.

Electrical signaling allows communication within and between different tissues and is necessary for the survival of multicellular organisms. The ionic transport that underlies transmembrane currents in cells is mediated by transporters and channels. Fast ionic transport through channels is typically modeled with a conductance-based formulation that describes current in terms of electrical drift without diffusion. In contrast, currents written in terms of drift and diffusion are not as widely used in the literature in spite of being more realistic and capable of displaying experimentally observable phenomena that conductance-based models cannot reproduce (e.g. rectification). The two formulations are mathematically related: conductance-based currents are linear approximations of drift-diffusion currents. However, conductance-based models of membrane potential are not first-order approximations of drift-diffusion models. Bifurcation analysis and numerical simulations show that the two approaches predict qualitatively and quantitatively different behaviors in the dynamics of membrane potential. For instance, two neuronal membrane models with identical populations of ion channels, one written with conductance-based currents, the other with drift-diffusion currents, undergo transitions into and out of repetitive oscillations through different mechanisms and for different levels of stimulation. These differences in excitability are observed in response to excitatory synaptic input, and across different levels of ion channel expression. In general, the electrophysiological profiles of membranes modeled with drift-diffusion and conductance-based models having identical ion channel populations are different, potentially causing the input-output and computational properties of networks constructed with these models to be different as well. The drift-diffusion formulation is thus proposed as a theoretical improvement over conductance-based models that may lead to more accurate predictions and interpretations of experimental data at the single cell and network levels.

Multiple outbreaks for the same pandemic: Local transportation and social distancing explain the different "waves" of A-H1N1pdm cases observed in México during 2009.

Influenza outbreaks have been of relatively limited historical interest in Mexico. The 2009 influenza pandemic not only changed Mexico's health priorities but also brought to the forefront some of the strengths and weaknesses of Mexico's epidemiological surveillance and public health system. A year later, Mexico's data show an epidemic pattern characterized by three "waves''. The reasons this three-wave patterns are theoretically investigated via models that incorporate Mexico's general trends of land transportation, public health measures, and the regular opening and closing of schools during 2009. The role of vaccination is also studied taking into account delays in access and limitations in the total and daily numbers of vaccines available. The research in this article supports the view that the three epidemic "waves" are the result of the synergistic interactions of three factors: regional movement patterns of Mexicans, the impact and effectiveness of dramatic social distancing measures imposed during the first outbreak, and the summer release of school children followed by their subsequent return to classes in the fall. The three "waves" cannot be explained by the transportation patterns alone but only through the combination of transport patterns and changes in contact rates due to the use of explicit or scheduled social distancing measures. The research identifies possible vaccination schemes that account for the school calendar and whose effectiveness are enhanced by social distancing measures. The limited impact of the late arrival of the vaccine is also analyzed.

Reduced models for the pacemaker dynamics of cardiac cells.

We introduce three- and two-dimensional biophysical models of cardiac excitability derived from a 14-dimensional model of the sinus venosus [Rasmusson, R., et al., 1990. Am. J. Physiol. 259, H352-369]. The reduced models capture normal pacemaking dynamics with a small complement of ionic currents. The two-dimensional model bears some similarities with the Morris-Lecar model [Morris, C., Lecar, H., 1981. Biophysical Journal, 35, 193-213]. Because they were reduced from a biophysical model, both models depend on parameters that were obtained from experimental data. Even though the correspondence with the original model is not exact, parameters may be adjusted to tune the reductions to fit experimental traces. As a consequence, unlike other generic low-dimensional models, the models introduced here provide a means to relate physiologically relevant characteristics of pacemaker potentials such as diastolic depolarization, plateau, and action potential frequency, to biophysical variables such as the relative abundance of membrane channels and channel kinetic rates. In particular, these models can lead to an explicit description of how the shape of cardiac action potentials depends on the relative contributions and states of inward and outward currents. By being physiologically derived and computationally efficient, the models presented in this article are useful tools for theoretical studies of excitability at the cellular and network levels.