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.

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.

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.

Dinámica del VIH-SIDA en Cali / The dynamics of HIV-AIDS in Cali

Para el estudio de la dinámica del VIH-SIDA en la ciudad de Cali, se uso el clásico modelo SIR para la transmisión de enfermedades infecciosas, donde la población total es dividida en Susceptibles, Infectados y Removidos, con los supuestos de que la transmisión sexual es el único medio de contagio y los individuos no se recuperan y mueren. Basándose en la información suministrada por la Secretaria Municipal de Salud de Santiago de Cali, DANE y Planeación Municipal, se estimaron los parámetros del modelo y del número reproductivo básico. Se realizaron simulaciones de algunos escenarios con el propósito de establecer tendencias a largo plazo de la enfermedad. Se estimaron los puntos de equilibrio del sistema y se analizaron las condiciones de estabilidad, encontrándose que actualmente el sistema posee dos puntos de equilibrio: E1: Libre de la enfermedad, de naturaleza inestable; E2: Endémico, de naturaleza asintóticamente estable. Tomando como condiciones iniciales la información del año 2008, se observo que la enfermedad tiende al equilibrio endémico después de 100 años. A través de simulaciones se logro establecer que al reducir la probabilidad de contagio entre susceptibles e infectados, la enfermedad tiende al equilibrio endémico de forma más lenta y se logra disminuir el número máximo de infectados y removidos.

The classical Kermack-Mckendric SIR model for infectious disease transmission was used for studying the dynamics of HIV-AIDS in the city of Cali; individuals were classified as being susceptible, infected or recovered (SIR) on the assumption that sexual transmission would be the only means of transmission and that individuals would not recover or die. The model's parameters and basic reproductive numbers were estimated using information supplied by the Santiago de Cali Municipal Secretariat of Health, the Colombian Statistics Bureau (DANE) and the Municipal Planning department. Some scenarios were simulated to establish long-term disease trends. The system's equilibrium points were estimated and stability conditions analyzed finding that the current system had two equilibrium points: unstable, disease-free (E1) and stable, endemically asymptotic (E2). Taking information from 2008 as initial conditions, it was observed that the disease would tend towards equilibrium after a 100 year endemic. Simulations suggested that the disease would tend towards endemic equilibrium more slowly by reducing the probability of contact between susceptible and infected individuals and that the maximum number of infected and recovered could also become reduced.

[The dynamics of HIV-AIDS in Cali]. / Dinámica del VIH-SIDA en Cali.

The classical Kermack-Mckendric SIR model for infectious disease transmission was used for studying the dynamics of HIV-AIDS in the city of Cali; individuals were classified as being susceptible, infected or recovered (SIR) on the assumption that sexual transmission would be the only means of transmission and that individuals would not recover or die. The model's parameters and basic reproductive numbers were estimated using information supplied by the Santiago de Cali Municipal Secretariat of Health, the Colombian Statistics Bureau (DANE) and the Municipal Planning department. Some scenarios were simulated to establish long-term disease trends. The system's equilibrium points were estimated and stability conditions analyzed finding that the current system had two equilibrium points: unstable, disease-free (E1) and stable, endemically asymptotic (E2). Taking information from 2008 as initial conditions, it was observed that the disease would tend towards equilibrium after a 100 year endemic. Simulations suggested that the disease would tend towards endemic equilibrium more slowly by reducing the probability of contact between susceptible and infected individuals and that the maximum number of infected and recovered could also become reduced.