Dobromir T. Dimitrov

Efficacy dilution in randomized placebo-controlled vaginal microbicide trials.

BackgroundTo date different vaginal gel microbicides have been evaluated in phase 2b/3 trials, but none have demonstrated effectiveness for preventing HIV infection. Failure to demonstrate effectiveness however does not necessarily indicate that a product is truly inefficacious, as several sources of efficacy dilution may compromise our ability to identify products that may have been truly efficacious.MethodsFor four individual sources of dilution, we describe the dilution mechanisms and quantify the expected effectiveness. An overall expected effectiveness that combines all sources of dilution in a trial is derived as well.ResultsUnder conditions that have been observed in recent microbicide trials, the overall expected effectiveness assuming an active gel with true efficacy of 50% and 75% are in the range of [16%; 33%] and [28%; 50%], respectively, when considering the four major sources of dilution. In contrast the diluting effect due to adherence alone (assuming an adherence of 80%) leads to higher expected effectiveness, 40% and 60% assuming an active gel with true efficacy of 50% and 75%, respectively. Individual sources of dilution may demonstrate a small effect when evaluated independently, but the overall dilution effect in a trial with several sources of dilution can be quite substantial.ConclusionCurrently planned phase 2b/3 microbicide trials of new candidate vaginal microbicides are not immune from these shortcomings. A good understanding of dilution effects is necessary to properly interpret microbicide trial results and to identify products worthy of further development and evaluation. Greater attention should be devoted to reducing and assessing the impact of efficacy dilution and to carefully selecting the effect size in the design of future trials.

Complete mathematical analysis of predator-prey models with linear prey growth and Beddington-DeAngelis functional response

The dynamics of a predator-prey model with a Beddington-DeAngelis functional response and linear intrinsic growth rate of the prey population is fully analyzed. Conditions on local and global stability of the interior equilibrium are established. The equilibria type are determined. All possible global asymptotic behaviors of the system are considered, including the determination of the extinction conditions and existence of periodic orbits. It is shown that mutual interference between predators can alone stabilize predator-prey interactions even when only a linear intrinsic growth rate of the prey population is considered in the mathematical model. Additional biological implications and a set of numerical simulations supporting the analysis are also presented.

Heterosexual Anal Intercourse: A Neglected Risk Factor for HIV?

Heterosexual anal intercourse confers a much greater risk of HIV transmission than vaginal intercourse, yet its contribution to heterosexual HIV epidemics has been under researched. In this article we review the current state of knowledge of heterosexual anal intercourse practice worldwide and identify the information required to assess its role in HIV transmission within heterosexual populations, including input measures required to inform mathematical models. We then discuss the evidence relating anal intercourse and HIV with sexual violence.

Nonstandard finite-difference schemes for general two-dimensional autonomous dynamical systems

Abstract General two-dimensional autonomous dynamical systems and their standard numerical discretizations are considered. Nonstandard stability-preserving finite-difference schemes based on the explicit and implicit Euler and the second-order Runge–Kutta methods are designed and analyzed. Their elementary stability is established theoretically and is also supported by a numerical example.

Nonstandard finite-difference methods for predator-prey models with general functional response

Predator-prey systems with linear and logistic intrinsic growth rate of the prey are analyzed. The models incorporate the mutual interference between predators into the functional response which stabilizes predator-prey interactions in the system. Positive and elementary stable nonstandard (PESN) finite-difference methods, having the same qualitative features as the corresponding continuous predator-prey models, are formulated and analyzed. The proposed numerical techniques are based on a nonlocal modeling of the growth-rate function and a nonstandard discretization of the time derivative. This discretization approach leads to significant qualitative improvements in the behavior of the numerical solution. In addition, it allows for the use of an essentially implicit method for the cost of an explicit method. Applications of the PESN methods to specific predator-prey systems are also presented.

Mathematical insights in evaluating state dependent effectiveness of HIV prevention interventions.

Mathematical models have been used to simulate HIV transmission and to study the use of preexposure prophylaxis (PrEP) for HIV prevention. Often a single intervention outcome over 10 years has been used to evaluate the effectiveness of PrEP interventions. However, different metrics express a wide variation over time and often disagree in their forecast on the success of the intervention. We develop a deterministic mathematical model of HIV transmission and use it to evaluate the public-health impact of oral PrEP interventions. We study PrEP effectiveness with respect to different evaluation methods and analyze its dynamics over time. We compare four traditional indicators, based on cumulative number or fractions of infections prevented, on reduction in HIV prevalence or incidence and propose two additional methods, which estimate the burden of the epidemic to the public-health system. We investigate the short and long term behavior of these indicators and the effects of key parameters on the expected benefits from PrEP use. Our findings suggest that public-health officials considering adopting PrEP in HIV prevention programs can make better informed decisions by employing a set of complementing quantitative metrics.

The future role of rectal and vaginal microbicides to prevent HIV infection in heterosexual populations: implications for product development and prevention

Objectives To compare the potential impact of rectal (RMB), vaginal (VMB) and bi-compartment (RVMB) (applied vaginally and protective during vaginal and anal intercourse) microbicides to prevent HIV in various heterosexual populations. To understand when a RMB is as useful than a VMB for women practicing anal intercourse (AI). Methods Mathematical model was used to assess the population-level impact (cumulative fraction of new HIV infections prevented (CFP)) of the three different microbicides in various intervention scenarios and prevalence settings. We derived the break-even RMB efficacy required to reduce a females cumulative risk of HIV infection by the same amount than a VMB. Results Under optimistic coverage (fast roll-out, 100% uptake), a 50% efficacious VMB used in 75% of sex acts in population without AI may prevent ∼33% (27, 42%) new total (men and women combined) HIV infections over 25 years. The 25-year CFP reduces to ∼25% (20, 32%) and 17% (13, 23%) if uptake decreases to 75% and 50%, respectively. Similar loss of impact (by 25%–50%) is observed if the same VMB is introduced in populations with 5%–10% AI and for RRRAI=4–20. A RMB is as useful as a VMB (ie, break-even) in populations with 5% AI if RRRAI=20 and in populations with 15%–20% AI if RRRAI=4, independently of adherence as long as it is the same with both products. The 10-year CFP with a RVMB is twofold larger than for a VMB or RMB when AI=10% and RRRAI=10. Conclusions Even low AI frequency can compromise the impact of VMB interventions. RMB and RVMB will be important prevention tools for heterosexual populations.

Comparative Effectiveness of Different Strategies of Oral Cholera Vaccination in Bangladesh: A Modeling Study

Background Killed, oral cholera vaccines have proven safe and effective, and several large-scale mass cholera vaccination efforts have demonstrated the feasibility of widespread deployment. This study uses a mathematical model of cholera transmission in Bangladesh to examine the effectiveness of potential vaccination strategies. Methods & Findings We developed an age-structured mathematical model of cholera transmission and calibrated it to reproduce the dynamics of cholera in Matlab, Bangladesh. We used the model to predict the effectiveness of different cholera vaccination strategies over a period of 20 years. We explored vaccination programs that targeted one of three increasingly focused age groups (the entire vaccine-eligible population of age one year and older, children of ages 1 to 14 years, or preschoolers of ages 1 to 4 years) and that could occur either as campaigns recurring every five years or as continuous ongoing vaccination efforts. Our modeling results suggest that vaccinating 70% of the population would avert 90% of cholera cases in the first year but that campaign and continuous vaccination strategies differ in effectiveness over 20 years. Maintaining 70% coverage of the population would be sufficient to prevent sustained transmission of endemic cholera in Matlab, while vaccinating periodically every five years is less effective. Selectively vaccinating children 1–14 years old would prevent the most cholera cases per vaccine administered in both campaign and continuous strategies. Conclusions We conclude that continuous mass vaccination would be more effective against endemic cholera than periodic campaigns. Vaccinating children averts more cases per dose than vaccinating all age groups, although vaccinating only children is unlikely to control endemic cholera in Bangladesh. Careful consideration must be made before generalizing these results to other regions.

Adaptive modeling of viral diseases in bats with a focus on rabies.

Abstract Many emerging and reemerging viruses, such as rabies, SARS, Marburg, and Ebola have bat populations as disease reservoirs. Understanding the spillover from bats to humans and other animals, and the associated health risks requires an analysis of the disease dynamics in bat populations. Traditional compartmental epizootic models, which are relatively easy to implement and analyze, usually impose unrealistic aggregation assumptions about disease-related structure and depend on parameters that frequently are not measurable in field conditions. We propose a novel combination of computational and adaptive modeling approaches that address the maintenance of emerging diseases in bat colonies through individual (intra-host) models of the response of the host to a viral challenge. The dynamics of the individual models are used to define survival, susceptibility and transmission conditions relevant to epizootics as well as to develop and parametrize models of the disease evolution into uniform and diverse populations. Applications of the proposed approach to modeling the effects of immunological heterogeneity on the dynamics of bat rabies are presented.

Analysis and numerical simulation of phytoplankton-nutrient systems with nutrient loss

The dynamics of a mathematical model of a layer of single phytoplankton species growing over a pool of nutrients, proposed by [A.H. Taylor, J.R.W. Harris, J. Aiken, The interaction of physical and biological process in a model of the vertical distribution of phytoplankton under stratification, Mar. Int. Ecohyrd., J.C. Nihoul (Ed.) 42 (1986) 313-330] is analyzed. Both cases of presence and absence of a phytoplankton in the water below the layer of interest are considered. Positive and elementary stable nonstandard (PESN) methods, having the same qualitative features as the corresponding continuous models, are formulated and analyzed. Biological implications and a set of numerical simulations supporting the mathematical and numerical analysis are also presented.