Juan Ospina

Using Phenomenological Models to Characterize Transmissibility and Forecast Patterns and Final Burden of Zika Epidemics

Background: The World Health Organization declared the ongoing Zika virus (ZIKV) epidemic in the Americas a Public Health Emergency of International Concern on February 1, 2016. ZIKV disease in humans is characterized by a “dengue-like” syndrome including febrile illness and rash. However, ZIKV infection in early pregnancy has been associated with severe birth defects, including microcephaly and other developmental issues. Mechanistic models of disease transmission can be used to forecast trajectories and likely disease burden but are currently hampered by substantial uncertainty on the epidemiology of the disease (e.g., the role of asymptomatic transmission, generation interval, incubation period, and key drivers). When insight is limited, phenomenological models provide a starting point for estimation of key transmission parameters, such as the reproduction number, and forecasts of epidemic impact. Methods: We obtained daily counts of suspected Zika cases by date of symptoms onset from the Secretary of Health of Antioquia, Colombia during January-April 2016. We calibrated the generalized Richards model, a phenomenological model that accommodates a variety of early exponential and sub-exponential growth kinetics, against the early epidemic trajectory and generated predictions of epidemic size. The reproduction number was estimated by applying the renewal equation to incident cases simulated from the fitted generalized-growth model and assuming gamma or exponentially-distributed generation intervals derived from the literature. We estimated the reproduction number for an increasing duration of the epidemic growth phase. Results: The reproduction number rapidly declined from 10.3 (95% CI: 8.3, 12.4) in the first disease generation to 2.2 (95% CI: 1.9, 2.8) in the second disease generation, assuming a gamma-distributed generation interval with the mean of 14 days and standard deviation of 2 days. The generalized-Richards model outperformed the logistic growth model and provided forecasts within 22% of the actual epidemic size based on an assessment 30 days into the epidemic, with the epidemic peaking on day 36. Conclusion: Phenomenological models represent promising tools to generate early forecasts of epidemic impact particularly in the context of substantial uncertainty in epidemiological parameters. Our findings underscore the need to treat the reproduction number as a dynamic quantity even during the early growth phase, and emphasize the sensitivity of reproduction number estimates to assumptions on the generation interval distribution.

Two-dimensional transport analysis of transdermal drug absorption with a non-perfect sink boundary condition at the skin-capillary interface

A transient percutaneous drug absorption model was solved in two dimensions. Clearance of the topically-applied pharmaceutical occured at the skin-capillary boundary. Timolol penetration profiles in the dermal tissue were produced revealing concentration gradients in the directions normal and parallel to the skin surface. Ninety-eight percent of the steady-state flux was reached after 85 h or four time constants. The analytical solution procedure agreed with published results. As the clearance rate increased relative to diffusion, the delivery rate and amount of drug absorbed into the bloodstream increased while the time to reach the equilibrium flux decreased. Researchers can apply the closed-form expressions to simulate the process, estimate key parameters and design devices that meet specific performance requirements.

TWO-DIMENSIONAL SOLUTION AND ANALYSIS OF A CYLINDRICAL MATRIX DEVICE WITH A CIRCULAR RELEASE AREA

A cylindrical device was analyzed using a Laplace transform–based method. The two-dimensional model represented a pharmaceutical agent uniformly distributed in a polymeric matrix surrounded by an impermeable layer. Molecules could be transferred only through a small hole centered at the top surface of the cylinder. A closed-form solution was obtained to help study the effects of design parameters and geometries on the cumulative amount of drug released. The latter variable increased with the mass transfer and diffusion coefficients and decreased with any increment in the devices length. The delivery rate was described by an effective time constant calculated from Laplace transforms. Reducing the orifice diameter or fabricating a longer system would delay transport of the medication. Simplified expressions for the release profile and the time constant were derived for special design cases.

Numerical Simulations of a Possible Hypercomputational Quantum Algorithm

The hypercomputers compute functions or numbers, or more generally solve problems or carry out tasks, that cannot be computed or solved by a Turing machine. Several numerical simulations of a possible hypercomputational algorithm based on quantum computations previously constructed by the authors are presented. The hypercomputability of our algorithm is based on the fact that this algorithm could solve a classically non-computable decision problem, the Hilbert’s tenth problem. The numerical simulations were realized for three types of Diophantine equations: with and without solutions in non-negative integers, and without solutions by way of various traditional mathematical packages.

Approximated analytical solution to an Ebola optimal control problem

ABSTRACT An analytical expression for the optimal control of an Ebola problem is obtained. The analytical solution is found as a first-order approximation to the Pontryagin Maximum Principle via the Euler–Lagrange equation. An implementation of the method is given using the computer algebra system Maple. Our analytical solutions confirm the results recently reported in the literature using numerical methods.

Prediction of in-vivo iontophoretic drug release data from in-vitro experiments-insights from modeling.

A strategy was developed to predict in-vivo plasma drug levels from data collected during in-vitro transdermal iontophoretic delivery experiments. The method used the principle of mass conservation and the Nernst-Planck flux equation to describe molecular transport across the skin. Distribution and elimination of the drug in the body followed a one- or two-compartment open model. Analytical expressions for the relaxation constant and plasma drug concentration were developed using Laplace transforms. The steady-state dermal flux was appropriate for predicting drug absorption under in-vivo conditions only when the time constant in the skin was far greater than its value in the blood compartment. A simulation study was conducted to fully assess the performance of estimations based on the equilibrium flux approximation. The findings showed that the normalized integral of squared error decreased exponentially as the ratio of the two time constants (blood/skin) increased. In the case of a single compartment, the error was reduced from 0.15 to 0.016 when the ratio increased from 10 to 100. The methodology was tested using plasma concentrations of a growth-hormone releasing factor in guinea pigs and naloxone in rats.

A FIRST-ORDER TIME CONSTANT ESTIMATION FOR NONLINEAR DIFFUSION PROBLEMS

A Laplace transform–based procedure was proposed to calculate the effective time constant for a class of nonlinear diffusion problems. The governing mathematical representation was first estimated with a linear model by omitting the nonlinear term. The solution to this problem was later introduced into the original equation, which was solved with Laplace transforms, resulting in a first-order approximation of the real systems behavior. A time constant was calculated using frequency-domain expressions. Two case studies were considered to illustrate the methodology. As the rate of heat supplied to a rod is raised, the speed at which the temperature reached an equilibrium value decreased. Increasing the maximum velocity in reaction-diffusion transport by a factor of three lowered the time constant by only 1.7%. The applications of this method range from biosensor dynamics to process control.

The dynamics of shrinking and expanding drug-loaded microspheres: A semi-empirical approach.

The dynamics of shrinking and expanding drug-loaded microspheres were studied using a diffusion equation in spherical coordinates. A movable boundary condition was incorporated as a convection term in the original model. The resulting convective-diffusive problem was solved using Laplace transform techniques with the Bromwich integral and the residue theorem. Analytical solutions were derived for the general case of shrinking or expanding microspheres and three particular kinetics expressions: linear growth, exponential swelling and exponential shrinking. Simulations show that microspheres with fast-swelling kinetics released their therapeutic cargo at a relatively slow rate in the first two cases. Ninety-nine percent of the medication was delivered at four times the effective time constant. In line with laboratory studies using bovine serum albumin, an increase in the shrinking rate led to a fast release of the medication from its carrier. The method was applied to analyze insulin transport through spherical Ca-alginate beads. A good agreement was noted between predicted and experimental data. The theoretical effective time constant was 114.0 min.

Tutte Polynomials and Topological Quantum Algorithms in Social Network Analysis for Epidemiology, Bio-surveillance and Bio-security

The Tutte polynomial and the Aharonov-Arab-Ebal-Landau algorithm are applied to Social Network Analysis (SNA) for Epidemiology, Biosurveillance and Biosecurity. We use the methods of Algebraic Computational SNA and of Topological Quantum Computation. The Tutte polynomial is used to describe both the evolution of a social network as the reduced network when some nodes are deleted in an original network and the basic reproductive number for a spatial model with bi-networks, borders and memories. We obtain explicit equations that relate evaluations of the Tutte polynomial with epidemiological parameters such as infectiousness, diffusivity and percolation. We claim, finally, that future topological quantum computers will be very important tools in Epidemiology and that the representation of social networks as ribbon graphs will permit the full application of the Bollobas-Riordan-Tutte polynomial with all its combinatorial universality to be epidemiologically relevant.

Stratifying the potential local transmission of Zika in municipalities of Antioquia, Colombia

To stratify and understand the potential transmission processes of Zika virus in Colombia, in order to effectively address the efforts on surveillance and disease control.