Modeling and biological control of mosquitoes

Abstract

Models can be useful at many different levels when considering complex issues such as biological control of mosquitoes. At an early stage, exploratory models are valuable in exploring the characteristics of an ideal biological control agent and for guidance in data collection. When more data are available, models can be used to explore alternative control strategies and the likelihood of success. There are few modeling studies that explicitly consider biological control in mosquitoes; however, there have been many theoretical studies of biological control in other insect systems and of mosquitoes and mosquito-borne diseases in general. Examples are used here to illustrate important aspects of designing, using and interpreting models. The stability properties of a model are valuable in assessing the potential of a biological control agent, but may not be relevant to a mosquito population with frequent environmental perturbations. The time scale and goal of proposed control strategies are important considerations when analyzing a model. The underlying biology of the mosquito host and the biological control agent must be carefully considered when deciding what to include in a model. Factors such as density dependent population growth in the host, the searching efficiency and aggregation of a natural enemy, and the resource base of both have been shown to influence the stability and dynamics of the interaction. Including existing mosquito control practices into a model is useful if biological control is proposed for locations with current insecticidal control. The development of Integrated Pest Management (IPM) strategies can be enhanced using modeling techniques, as a wide variety of options can be simulated and examined. Models can also be valuable in comparing alternate routes of disease transmission and to investigate the level of control needed to reduce transmission.

Fig. 1

Stability and control in populations. a) Examples of stable equilibria: If an equilibrium point is stable and constant (dashed line), the population size is constant and will return to the same size following a disturbance (imposed at the time marked by the arrow; e.g., control reducing the population). There can also be cyclical equilibria (solid black line), where the population size cycles between different values. Again, the population returns to this same cycle following a disturbance (in this case, an increase in the population; this could be caused by environmental conditions, a supplemental release of a biocontrol agent, etc.). For illustration, an unstable population (grey line) is shown; in this case the population fluctuates with no equilibrium. b) Examples of unstable equilibria: If a population is at an unstable equilibrium, the size of the population will not return to the original value following a disturbance (arrow). It may settle to a new equilibrium point, or become unstable. Two possibilities are illustrated here: an unstable, constant equilibrium settling to a new, constant equilibrium (which may be stable or unstable) following a disturbance, and an equilibrium cycle becoming chaotic following a disturbance. c) Some possible outcomes of control measures: A stable equilibrium is not always the ideal goal for control. Here, a population at equilibrium is disturbed by a control strategy and settles to a new equilibrium; however, the new population size is still above the threshold for concern (set by economics, disease transmission, or nuisance issues). Conversely, an unstable population with unpredictable dynamics could be depressed below the threshold. Other scenarios are possible, including a controlled population that undergoes outbreaks that exceed the threshold.