Dobromir T. Dimitrov

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General multi-dimensional autonomous dynamical systems and their numerical discretizations are considered. Nonstandard stability-preserving finite-difference schemes based on the θ-methods and the second-order Runge-Kutta methods are designed and analyzed. Their elementary stability is established theoretically and is also supported by a set of numerical(More)
BACKGROUND To 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(More)
There are bacteria that can form strong biofilms in porous media. These biofilms can be used as biobarriers to restrict the flow of pollutants. For certain contaminants, a second species of bacteria that can actually react with the contaminants can be added to the biobarrier to actually degrade the pollutants. We propose some mathematical models for the(More)
Temperate-zone bats are subject to serious energetic constraints due to their high surface area to volume relations, the cost of temperature regulation, the high metabolic cost of flight, and the seasonality of their resources. We present a novel, multilevel theoretical approach that integrates information on bat biology collected at a lower level of(More)
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(More)
BACKGROUND Four clinical trials have shown that oral and topical pre-exposure prophylaxis (PrEP) based on tenofovir may be effective in preventing HIV transmission. The expected reduction in HIV transmission and the projected prevalence of drug resistance due to PrEP use vary significantly across modeling studies as a result of the broad spectrum of(More)