Comparing the long-term persistence of different Wolbachia strains after the release of bacteria-carrying mosquitoes.

This paper proposes a bidimensional modeling framework for Wolbachia invasion, assuming imperfect maternal transmission, incomplete cytoplasmic incompatibility, and direct infection loss due to thermal stress. Our model adapts to various Wolbachia strains and retains all properties of higher-dimensional models. The conditions for the durable coexistence of Wolbachia-carrying and wild mosquitoes are expressed using the model's parameters in a compact closed form. When the Wolbachia bacterium is locally established, the size of the remanent wild population can be assessed by a direct formula derived from the model. The model was tested for four Wolbachia strains undergoing laboratory and field trials to control mosquito-borne diseases: wMel, wMelPop, wAlbB, and wAu. As all these bacterial strains affect the individual fitness of mosquito hosts differently and exhibit different levels of resistance to temperature variations, the model helped to conclude that: (1) the wMel strain spreads faster in wild mosquito populations; (2) the wMelPop exhibits lower resilience but also guarantees the smallest size of the remanent wild population; (3) the wAlbB strain performs better at higher ambient temperatures than others; (4) the wAu strain is not sustainable and cannot persist in the wild mosquito population despite its resistance to high temperatures.

Monotonicity properties arising in a simple model of Wolbachia invasion for wild mosquito populations.

In this paper, we propose a simplified bidimensional Wolbachia infestation model in a population of Aedes aegypti mosquitoes, preserving the main features associated with the biology of this species that can be found in higher-dimensional models. Namely, our model represents the maternal transmission of the Wolbachia symbiont, expresses the reproductive phenotype of cytoplasmic incompatibility, accounts for different fecundities and mortalities of infected and wild insects, and exhibits the bistable nature leading to the so-called principle of competitive exclusion. Using tools borrowed from monotone dynamical system theory, in the proposed model, we prove the existence of an invariant threshold manifold that allows us to provide practical recommendations for performing single and periodic releases of Wolbachia-carrying mosquitoes, seeking the eventual elimination of wild insects that are capable of transmitting infections to humans. We illustrate these findings with numerical simulations using parameter values corresponding to the wMelPop strain of Wolbachia that is considered the best virus blocker but induces fitness loss in its carriers. In these tests, we considered multiple scenarios contrasting a periodic release strategy against a strategy with a single inundative release, comparing their effectiveness. Our study is presented as an expository and mathematically accessible tool to study the use of Wolbachia-based biocontrol versus more complex models.

A synthesized model of tuberculosis transmission featuring treatment abandonment.

In this paper, we propose and justify a synthesized version of the tuberculosis transmission model featuring treatment abandonment. In contrast to other models that account for the treatment abandonment, our model has only four state variables or classes (susceptible, latent, infectious, and treated), while people abandoning treatment are not gathered into an additional class. The proposed model retains the core properties that are highly desirable in epidemiological modeling. Namely, the disease transmission dynamics is characterized by the basic reproduction number $ \mathscr{R}_0 $, a threshold value that determines the number of possible steady states and their stability properties. It is shown that the disease-free equilibrium is globally asymptotically stable (GAS) only if $ \mathscr{R}_0 < 1 $, while a strictly positive endemic equilibrium exists and is GAS only if $ \mathscr{R}_0 > 1. $ Analysis of the dependence of $ \mathscr{R}_0 $ on the treatment abandonment rate shows that a reduction of the treatment abandonment rate has a positive effect on the disease incidence and results in avoiding disease-related fatalities.

Optimal release programs for dengue prevention using Aedes aegypti mosquitoes transinfected with wMel or wMelPop Wolbachia strains.

In this paper, we propose a dengue transmission model of SIR(S)-SI type that accounts for two sex-structured mosquito populations: the wild mosquitoes (males and females that are Wolbachia-free), and those deliberately infected with either wMel or wMelPop strain of Wolbachia. This epidemiological model has four possible outcomes: with or without Wolbachia and with or without dengue. To reach the desired outcome, with Wolbachia and without dengue, we employ the dynamic optimization approach and then design optimal programs for releasing Wolbachia-carrying male and female mosquitoes. Our discussion is focused on advantages and drawbacks of two Wolbachia strains, wMelPop and wMel, that are recommended for dengue prevention and control. On the one hand, the wMel strain guarantees a faster population replacement, ensures durable Wolbachia persistence in the wild mosquito population, and requiters fewer releases. On the other hand, the wMelPop strain displays better results for averting dengue infections in the human population.

Implementation of control strategies for sterile insect techniques.

In this paper, we propose a sex-structured entomological model that serves as a basis for design of control strategies relying on releases of sterile male mosquitoes (Aedes spp) and aiming at elimination of the wild vector population in some target locality. We consider different types of releases (constant and periodic impulsive), providing sufficient conditions to reach elimination. However, the main part of the paper is focused on the study of the periodic impulsive control in different situations. When the size of wild mosquito population cannot be assessed in real time, we propose the so-called open-loop control strategy that relies on periodic impulsive releases of sterile males with constant release size. Under this control mode, global convergence towards the mosquito-free equilibrium is proved on the grounds of sufficient condition that relates the size and frequency of releases. If periodic assessments (either synchronized with the releases or more sparse) of the wild population size are available in real time, we propose the so-called closed-loop control strategy, under which the release size is adjusted in accordance with the wild population size estimate. Finally, we propose a mixed control strategy that combines open-loop and closed-loop strategies. This control mode renders the best result, in terms of overall time needed to reach elimination and the number of releases to be effectively carried out during the whole release campaign, while requiring for a reasonable amount of released sterile insects.

Sustainable thresholds for cooperative epidemiological models.

In this paper, we introduce a method for computing sustainable thresholds for controlled cooperative models described by a system of ordinary differential equations, a property shared by a wide class of compartmental models in epidemiology. The set of sustainable thresholds refers to constraints (e.g., maximal "allowable" number of human infections; maximal "affordable" budget for disease prevention, diagnosis and treatments; etc.), parameterized by thresholds, that can be sustained by applying an admissible control strategy starting at the given initial state and lasting the whole period of the control intervention. This set, determined by the initial state of the dynamical system, virtually provides useful information for more efficient (or cost-effective) decision-making by exhibiting the trade-offs between different types of constraints and allowing the user to assess future outcomes of control measures on transient behavior of the dynamical system. In order to accentuate the originality of our approach and to reveal its potential significance in real-life applications, we present an example relying on the 2013 dengue outbreak in Cali, Colombia, where we compute the set of sustainable thresholds (in terms of the maximal "affordable" budget and the maximal "allowable" levels of active infections among human and vector populations) that could be sustained during the epidemic outbreak.

Assessing the effects of daily commuting in two-patch dengue dynamics: A case study of Cali, Colombia.

There are many infectious diseases that can be spread by daily commuting of people and dengue fever is one of them. The absence of vaccine and irregularities in ongoing vector control programs make this disease the most frequent and persistent in many tropical and subtropical regions of the world. This paper targets to access the effects of daily commuting on dengue transmission dynamics by using a deterministic two-patch model fitted to observed data gathered in Cali, Colombia where dengue fever is highly persistent and exhibits endemo-epidemic patterns. The two-patch dengue transmission model with daily communing of human residents between patches (that is, between the city and its suburban areas) is presented using the concept of residence times, which certainly affect the disease transmission rates by inducing variability in human population sizes and vectorial densities at each patch. The same modeling framework is applied to two primary scenarios (epidemic outbreaks and endemic persistence of the disease) and for each scenario two coupling cases (one-way and asymmetric commuting) with different inflow and outflow intensities are analyzed. The concept of effective vectorial density, introduced in this paper, allows to explain in very simple terms why the daily commuting affects quite differently the dengue morbidity among human residents in both patches. In particular, residents of the patch with a greater share of incoming than outgoing commuters may actually "benefit" from inflow of daily commuter by avoiding a considerable number of infections. However, residents of the patch with a greater share of outgoing than incoming commuters, especially those who stay at home patch, incur more risk of getting infected. Additionally, the model shows that daily commuting enhance the total number of human infections acquired in both patches and may even provoke an epidemic outbreak in one patch while moderately lowering the level of the disease persistence in another patch.

Early Effects of Ionizing Radiation on the Collagen Hierarchical Structure of Bladder and Rectum Visualized by Atomic Force Microscopy.

Radiation therapy, widely used in the treatment of a variety of malignancies in the pelvic area, is associated with inevitable damage to the surrounding healthy tissues. We have applied atomic force microscopy (AFM) to track the early damaging effects of ionizing radiation on the collagen structures in the experimental animals' bladder and rectum. The first signs of the low-dose radiation (2 Gy) effect were detected by AFM as early as 1 week postirradiation. The observed changes were consistent with initial radiation destruction of the protein matrix. The alterations in the collagen fibers' packing 1 month postirradiation were indicative of the onset of fibrotic processes. The destructive effect of higher radiation doses was probed 1 day posttreatment. The severity of the radiation damage was proportional to the dose, from relatively minor changes in the collagen packing at 8 Gy to the growing collagen matrix destruction at higher doses and complete three-dimensional collagen network restructuring towards fibrotic-type architecture at the dose of 22 Gy. The AFM study appeared superior to the optical microscopy-based studies in its sensitivity to early radiation damage of tissues, providing valuable additional information on the onset and development of the collagen matrix destruction and remodeling.

Optimal control approach for establishing wMelPop Wolbachia infection among wild Aedes aegypti populations.

Wolbachia-based biocontrol has recently emerged as a potential method for prevention and control of dengue and other vector-borne diseases. Major vector species, such as Aedes aegypti females, when deliberately infected with Wolbachia become less capable of getting viral infections and transmitting the virus to human hosts. In this paper, we propose an explicit sex-structured population model that describes an interaction of uninfected (wild) male and female mosquitoes and those deliberately infected with wMelPop strain of Wolbachia in the same locality. This particular strain of Wolbachia is regarded as the best blocker of dengue and other arboviral infections. However, wMelPop strain of Wolbachia also causes the loss of individual fitness in Aedes aegypti mosquitoes. Our model allows for natural introduction of the decision (or control) variable, and we apply the optimal control approach to simulate wMelPop Wolbachia infestation of wild Aedes aegypti populations. The control action consists in continuous periodic releases of mosquitoes previously infected with wMelPop strain of Wolbachia in laboratory conditions. The ultimate purpose of control is to find a tradeoff between reaching the population replacement in minimum time and with minimum cost of the control effort. This approach also allows us to estimate the number of Wolbachia-carrying mosquitoes to be released in day-by-day control action. The proposed method of biological control is safe to human health, does not contaminate the environment, does not make harm to non-target species, and preserves their interaction with mosquitoes in the ecosystem.

Ross McDonald: Un modelo para la dinámica del dengue en Cali, Colombia / Ross-Macdonald: A model for the dengue dynamic in Cali, Colombia

El dengue es una infección transmitida por mosquitos que se presenta en todas las regiones tropicales y subtropicales del planeta. En años recientes, la transmisión ha aumentado de manera predominante en zonas urbanas y semiurbanas y se ha convertido en un importante problema de salud pública. El Instituto Nacional de Salud-INS, ubicó a Cali como el municipio con más casos de dengue en Colombia. De acuerdo con el INS, en la ciudad de Cali, hasta la semana epidemiológica 18 (del 28 de abril al 4 de mayo de 2013), se han notificado 5 134 casos de dengue y 171 de dengue grave. En este trabajo se presenta la descripción del modelo Ross McDonald, el análisis cualitativo de dicho modelo, y el análisis de sensibilidad del modelo a cambios en sus parámetros. Y base en el ajuste del modelo obtenido para los casos presentados en el 2010, se hacen y analizan simulaciones de posibles escenarios de brotes epidémicos en la ciudad de Cali.(AU)

Dengue is an infection transmitted by mosquitoes and is present in all tropical and subtropical regions of the planet. In recent years, the transmission of the disease has increased, predominantly in urban and semi-urban areas, and has become an important public health problem. The National Health Institute (Instituto Nacional de Salud-INS) determined Cali to be the municipality with the most cases of dengue in Colombia. According to the INS, up to epidemiological week 18 (April 28 to May 4, 2013) 5 134 cases of dengue -and 171 cases of severe dengue- have been reported. This study presents a description of the Ross-Macdonald model, and qualitative analysis of this model, and an analysis of the sensitivity of the model to changes in its parameters. Based on the adjustment of the model obtained for cases that occurred in 2010, simulations of possible scenarios of epidemic outbreaks in the city of Cali are created and analyzed.(AU)

[Ross-Macdonald: A model for the dengue dynamic in Cali, Colombia]. / Ross McDonald: Un modelo para la dinámica del dengue en Cali, Colombia.

Dengue is an infection transmitted by mosquitoes and is present in all tropical and subtropical regions of the planet. In recent years, the transmission of the disease has increased, predominantly in urban and semi-urban areas, and has become an important public health problem. The National Health Institute (Instituto Nacional de Salud-INS) determined Cali to be the municipality with the most cases of dengue in Colombia. According to the INS, up to epidemiological week 18 (April 28 to May 4, 2013) 5 134 cases of dengue -and 171 cases of severe dengue- have been reported. This study presents a description of the Ross-Macdonald model, and qualitative analysis of this model, and an analysis of the sensitivity of the model to changes in its parameters. Based on the adjustment of the model obtained for cases that occurred in 2010, simulations of possible scenarios of epidemic outbreaks in the city of Cali are created and analyzed.

Age-related changes in angiogenesis in human dermis.

Present research is aimed to examine the number of dermal blood vessels, vascular endothelial growth factor (VEGF), delta-like ligand 4(Dll4) and Jagged-1 (Jag-1) in dermal blood vessels of human from 20weeks of pregnancy to 85years old. Numbers and proliferative activity of dermal fibroblast-like cells were also examined. Blood vessels were viewed with immunohistochemical staining for von Willebrand factor or CD31. VEGF, Dll4, Jag-1, and proliferating cell nuclear antigen (PCNA) were detected immunohistochemically. Results showed that the numbers of fibroblast-like cells, PCNA positive fibroblast-like cells, von Willebrand factor positive or CD31 positive blood vessels in dermis are dramatically decreased with age. The intensity of immunohistochemical staining for VEGF or Jag-1 in blood vessels of dermis is increased from antenatal to deep old period. The degree of immunohistochemical staining of dermal blood vessels for Dll4 has gone up from 20-40weeks of pregnancy to early life period (0-20years), and further decreased below antenatal values. Age-related decrease in the number of dermal blood vessels is suggested to be due to an impairment of VEGF signaling and to be mediated by Dll4 and Jag-1. It may be supposed that diminishing in blood supply of dermis occurring with age is a cause of a decrease in the number and proliferative pool of dermal fibroblasts.

Optimal policies aimed at stabilization of populations with logistic growth under human intervention.

This work examines both positive and negative impacts that economic growth may have on the ecological dynamics and stability of a single biological species. Local extinction of the species may force the social planner to implement defensive expenditures aimed at conservation of the species population by means of habitat protection. The latter may lead to an ecological equilibrium that will be different from the natural equilibrium that would have arisen in the absence of human intervention. Moreover, the existence of such equilibrium is formally demonstrated and its stability properties are revised. Additionally, optimal-choice decision policies are constructed on the basis of Pontryagin's maximum principle. Under such policies together with initial abundance of the species, the growth trajectories will move the system towards the fixed point of maximum species abundance.

Age-related changes in proliferation, the numbers of mast cells, eosinophils, and cd45-positive cells in human dermis.

Skin aging is an extremely important medical and social problem in the modern world. Therefore, a goal of the present work was to estimate changes in the numbers of fibroblast-like cells, proliferating cells nuclear antigen-positive cells, CD45-positive cells, mast cells, and eosinophils in human dermis at different ages. Skin specimens from human fetuses that died antenatally from 20 to 40 weeks of pregnancy and humans who died from different causes from 1 day to 85 years of life were used for the study. Results showed a decrease in a total number and the number of proliferating cells nuclear antigen-positive fibroblast-like cells in dermis with progression of age. The numbers of CD45-positive cells and mast cells are gradually increased with aging. Eosinophils are almost absent in dermis independently on age. Mast cells are probably a main factor that potentially can be involved in tissue damage and aging changes in skin. Mast cells should be regarded as an important target for anti-aging therapy.