Hyun Mo Yang

Assessing the effects of temperature on the population of Aedes aegypti , the vector of dengue

Dengue is a vector-borne disease transmitted by the mosquito Aedes aegypti. The incidence of dengue disease shows a clear dependence on seasonal variation. How does the temperature affect the incidence? We addressed this question indirectly by estimating the size of the A. aegypti population for different temperatures applying population dynamics theory. In order to achieve this objective we designed temperature-controlled experiments to assess the entomological parameters regarding the mosquitos life-cycle at different temperatures. By obtaining the mortality, transition and oviposition rates for different stages of the life-cycle of the mosquito we were able to calculate the basic offspring number Q(0), which is the capacity of vector reproduction and ultimately gives the size of the vector population.

Optimal control of Aedes aegypti mosquitoes by the sterile insect technique and insecticide

We present a mathematical model to describe the dynamics of mosquito population when sterile male mosquitoes (produced by irradiation) are introduced as a biological control, besides the application of insecticide. In order to analyze the minimal effort to reduce the fertile female mosquitoes, we search for the optimal control considering the cost of insecticide application, the cost of the production of irradiated mosquitoes and their delivery as well as the social cost (proportional to the number of fertilized females mosquitoes). The optimal control is obtained by applying the Pontryagins Maximum Principle.

Malaria transmission model for different levels of acquired immunity and temperature-dependent parameters (vector)

OBJECTIVE Describe the overall transmission of malaria through a compartmental model, considering the human host and mosquito vector. METHODS A mathematical model was developed based on the following parameters: human host immunity, assuming the existence of acquired immunity and immunological memory, which boosts the protective response upon reinfection; mosquito vector, taking into account that the average period of development from egg to adult mosquito and the extrinsic incubation period of parasites (transformation of infected but non-infectious mosquitoes into infectious mosquitoes) are dependent on the ambient temperature. RESULTS The steady state equilibrium values obtained with the model allowed the calculation of the basic reproduction ratio in terms of the models parameters. CONCLUSIONS The model allowed the calculation of the basic reproduction ratio, one of the most important epidemiological variables.

Describing the geographic spread of dengue disease by traveling waves

Dengue is a human disease transmitted by the mosquito Aedes aegypti. For this reason geographical regions infested by this mosquito species are under the risk of dengue outbreaks. In this work, we propose a mathematical model to study the spatial dissemination of dengue using a system of partial differential reaction-diffusion equations. With respect to the human and mosquito populations, we take into account their respective subclasses of infected and uninfected individuals. The dynamics of the mosquito population considers only two subpopulations: the winged form (mature female mosquitoes), and an aquatic population (comprising eggs, larvae and pupae). We disregard the long-distance movement by transportation facilities, for which reason the diffusion is considered restricted only to the winged form. The human population is considered homogeneously distributed in space, in order to describe localized dengue dissemination during a short period of epidemics. The cross-infection is modeled by the law of mass action. A threshold value as a function of the models parameters is obtained, which determines the rate of dengue dissemination and the risk of dengue outbreaks. Assuming that an area was previously colonized by the mosquitoes, the rate of disease dissemination is determined as a function of the models parameters. This rate of dissemination of dengue disease is determined by applying the traveling wave solutions to the corresponding system of partial differential equations.

Rubella seroepidemiology in a non-immunized population of São Paulo State, Brazil.

A rubella serological survey of 476 individuals selected by cluster sampling technique from Caieiras, a small town located in the outskirts of São Paulo city, southeastern Brazil, was carried out over the period November 1990-January 1991. The aim of the study was to characterize rubella epidemiology in a representative non-immunized community in south east Brazil. The survey comprised a seroprevalence study, stratified by age (0-40 years) and a seroconversion study of rubella vaccine in non-infected children below 2 years of age. Mathematical techniques were applied to resultant data sets to determine the age dependent rates of decay in the proportion of individuals with maternally derived antibodies, vaccine seroconversion, and infection of susceptibles, termed the force of infection, and to estimate the average age at first infection.

Assessing the effects of vector control on dengue transmission

The dengue virus is an arbovirus transmitted to humans through mosquito Aedes aegypti. To describe the dynamics of dengue disease within these two populations we develop a compartment model taking into account chemical controls and mechanical control applied on the mosquitoes, which are the currently available controlling mechanisms to prevent dengue disease. To mimic seasonal variations, some parameters of the model are allowed to depend on time in order to divide a calendar year in favorable and unfavorable periods regarded to the development of vector population.

A model-based design of a vaccination strategy against rubella in a non-immunized community of São Paulo State, Brazil

A mixed vaccination strategy against rubella is proposed. We describe how the vaccination strategy was designed with the help of mathematical techniques. The strategy was designed for application in a non-immunized community of the State of São Paulo, Brazil, and was implemented by local health authorities in 1992. This strategy comprises a pulse vaccination campaign, covering the age interval between 1 and 10 years, followed by the introduction of the vaccine in the immunization calendar at 15 months of age. The expected impact of the proposed strategy is discussed.

Spatial spreading of West Nile Virus described by traveling waves.

In this work, we propose a spatial model to analyze the West Nile Virus propagation across the USA, from east to west. West Nile Virus is an arthropod-borne flavivirus that appeared for the first time in New York City in the summer of 1999 and then spread prolifically among birds. Mammals, such as humans and horses, do not develop sufficiently high bloodstream titers to play a significant role in the transmission, which is the reason to consider the mosquito-bird cycle. The model aims to study this propagation based on a system of partial differential reaction-diffusion equations taking the mosquito and the avian populations into account. Diffusion and advection movements are allowed for both populations, being greater in the avian than in the mosquito population. The traveling wave solutions of the model are studied to determine the speed of disease dissemination. This wave speed is obtained as a function of the models parameters, in order to assess the control strategies. The propagation of West Nile Virus from New York City to California state is established as a consequence of the diffusion and advection movements of birds. Mosquito movements do not play an important role in the disease dissemination, while bird advection becomes an important factor for lower mosquito biting rates.

Assessing the effects of global warming and local social and economic conditions on the malaria transmission

OBJECTIVE To show how a mathematical model can be used to describe and to understand the malaria transmission. METHODS The effects on malaria transmission due to the impact of the global temperature changes and prevailing social and economic conditions in a community were assessed based on a previously presented compartmental model, which describes the overall transmission of malaria. RESULTS/CONCLUSIONS The assessments were made from the scenarios produced by the model both in steady state and dynamic analyses. Depending on the risk level of malaria, the effects on malaria transmission can be predicted by the temperature ambient or local social and-economic conditions.

Follow up estimation of Aedes aegypti entomological parameters and mathematical modellings

The dengue virus is a vector-borne disease transmitted by mosquito Aedes aegypti and the incidence is strongly influenced by temperature and humidity which vary seasonally. To assess the effects of temperature on dengue transmission, mathematical models are developed based on the population dynamics theory. However, depending on the hypotheses of the modelling, different outcomes regarding to the risk of epidemics are obtained. We address this question comparing two simple models supplied with models parameters estimated from temperature-controlled experiments, especially the entomological parameters regarded to the mosquitos life cycle in different temperatures. Once obtained the mortality and transition rates of different stages comprising the life cycle of mosquito and the oviposition rate, we compare the capacity of vector reproduction (the basic offspring number) and the risk of infection (basic reproduction number) provided by two models. The extended model, which is more realistic, showed that both mosquito population and dengue risk are situated at higher values than the simplified model, even that the basic offspring number is lower.