Maximum productivity of Aedes aegypti (Diptera: Culicidae) based on the dynamics of its aquatic state

This paper develops a mathematical framework to estimate the average productivity of Aedes aegypti (Diptera: Culicidae) in artificial breeding sites, focusing on open household water-storage containers typical of areas with limited access to piped water. We introduce the effective larval displacement volume and, using data from a controlled experiment conducted under climatic conditions favorable for mosquito larval development, derive stage-specific carrying capacities as functions of container dimensions and water volume. The mosquito life cycle is represented by a dynamic population model with seven biologically grounded stages (egg, four larval instars, pupa, and adult) that incorporates nonlinear oviposition, asynchronous hatching, and density-dependent larval competition. Assuming favorable climatic conditions the model admits a unique, globally asymptotically stable equilibrium, so the equilibrium adult population provides a robust measure of breeding-site productivity. From this equilibrium we obtain a closed-form approximation for average adult productivity in terms of water-column height and container perimeter, and apply it to storage containers commonly used in Latin-America: buckets, plastic barrels, water tanks, and cement storage piles. The results indicate that productivity varies only weakly with container size, suggesting that consolidating stored water into a single large container, rather than several smaller ones, may reduce overall mosquito emergence. Because all estimates are derived under optimal environmental and water-quality conditions, they should be interpreted as upper bounds for productivity under less favorable or adverse settings, a distinction that is essential for real-world vector-control planning. Overall, the proposed approach offers an operational tool for quantifying productivity in domestic water-storage breeding sites.