Predator-Prey Model for Analysis of Aedes Aegypti Population Dynamics in Cali, Colombia

Abstract

In this paper, we introduce a predator-prey model to analyze the population dynamics of the Aedes aegypti mosquito which is fairly blamed for the transmission of dengue in Cali, Colombia. The model describes an interaction of an aquatic predacious species deliberately introduced into local mosquito breeding habitat, where the Aedes aegypti immature stages (eggs, larvae, and pupae) are already present and constitute the prey population. The model also accounts for local population of adult female mosquitoes (or mature stage) emerging from the breeding site. This population is considered as a target for reduction by deploying an adequate predacious species since only female mosquitoes are held responsible for transmission of dengue and other vector-borne diseases. Having analyzed the model, we have derived the mosquito survival threshold with predation as a function of predator's biological characteristics. The model's parameters were adjusted to the average seasonal temperatures of Cali, Colombia and explicit conditions for biological characteristics of prospective efficient predators were established. Numerical simulation with introduction of an efficient predacious species in local mosquito breeding habitats revealed the possibility of eventual mosquito extinction in such localities. Finally, some particular biological species were proposed as potential candidates for efficient predators.

Estimación de los parámetros de dos modelos para la dinámica del dengue y su vector en Cali, Colombia

“…De otro lado, el depredador presenta un crecimiento logístico y, a diferencia de [9], en este trabajo, consideramos un incremento (ψm q ) en el crecimiento intrínseco del depredador asociado a la interacción con la presa, como se planteó en [11]. [Tercera ecuación en (1)].…”

“…Para terminar esta parte, debemos anotar, primero, que los valores de los parámetros aquí estimados son válidos no solo para el modelo (1) sino tambien para cualquier otro modelo donde tengan el mismo significado; y segundo, que los otros dos parámetros del modelo (1), las capacidades de carga tanto de los estadios inmaduros como del depredador, pueden tomarse en forma relativa la una con la otra, según la situación que se desee modelar (Por ejemplo, ver Sección 6 en [11]).…”

“…Luego, en la Sección 4, describimos el modelo de Ross-Macdonald adaptado para el análisis de las poblaciones de humanos y mosquitos infectados por el virus del dengue y, en la Sección 5, presentamos la estimación de los parámetros epidemiológicos del dengue en Cali usando la solución de mínimos cuadrados en el ajuste de los resultados del modelo y los casos reportados de dengue en la ciudad de Cali según la SSMC. Conviene notar que el estudio de la estabilidad de ambos modelos y la sensibilidad de sus parámetros estan presentados en [11], [12]. En el Apéndice, hacemos un análisis comparativo de los polinomios determinados en [6], [7], y los calculados y usados en la Sección 3 para estimar los parámetros entomológicos del mosquito para la ciudad de Cali.…”

Zika Outbreak in 2016: Understanding Brazilian Social Inequalities through Urban Spatial Analysis and their Consequences to Health

“…When temperature raises nearly everything about "Aedesaegypti" biology speeds up. The adult stage, for example, can range from two weeks to a month depending on environmental conditions [53,54] Under moderate temperature fluctuations [55], the hotter the air the longer the mosquito survives as an adult to take blood, develop eggs, and lay those eggs in an aquatic setting. Laid eggs can survive for more than a year in a dry weather conditions; however they hatch immediately once submerged in water (Kearney et al, 2009), making the control of mosquito extremely challenging.…”

Interaction between Spatial and Temporal Scales for Entomological Field Data: Analysis of Aedes Aegypti Oviposition Series

“…Traditional control measures include: a) The elimination of larval habitats, using chemical treatment, to prevent adult production and b) The application of spatial aerosol insecticides to reduce adult population density [5]. Despite of the resistance vector and environmental concerns, chemical control still remains the main strategy of vector control programs; however the World Health Organization (WHO) and the Pan-American Health Organization (PAHO) jointly promote its combination with other non-chemical vector control strategies [6]. For this reason, the identification of vector "hot spots" is an important key to design preventive program tools [7].…”