Methods for prophylactic management of West Nile virus using a stage‐structured avian host‐vector model with vaccination, larvicide, and adulticide

Abstract

West Nile virus (WNV) is a vector‐borne disease spread primarily between birds and mosquitoes. In the United States, the main methods used to control WNV are aimed at lowering the vector population through reducing births (larvicide) or increasing the mortality of adults (adulticide). We investigate the potential of a novel control, vaccination of newborn birds (nestlings). We first apply standard optimal control (OC) methodology to a nonautonomous differential equation model for WNV transmission incorporating avian stage structure and allowing larvicide, adulticide, and nestling vaccination. We convert the continuous OC results to practical advice that accounts for restrictions on the frequency of control application in the field. We then develop an alternative optimization algorithm using genetic algorithms and compare control advice for various budget constraints. We find that vaccination is recommended, provided budgets are sufficiently high, and explore how differences in control efficacy and vector biting rates on host stages affect our results. Recommendations for Resource Managers: Genetic algorithms are able to incorporate practical restrictions on control application as well as budget constraints. Advice depends on the efficacies of controls as well as model parameters. At high‐efficacy estimates, adulticide is recommended for low budgets. Vaccination is recommended when budgets are sufficiently high, and sooner for scenarios where nestling hosts have increased vector exposure. If vector control has low efficacy and nestlings have increased vector exposure relative to older hosts, including vaccination may reduce levels of infectious mosquitoes below those resulting from high‐efficacy vector control alone.

Implicit versus explicit control strategies in models for vector-borne disease epidemiology

“…Optimal control theory provides a set of mathematical tools which, when applied to vector-borne disease models, can be used to find control protocols for achieving a control objective, such as R 0 < 1, which minimizes a cost of control, or to find control protocols which optimally balance a disease cost with a cost of control. Typically, for human intervention strategies, the cost of control is taken to be a monetary cost associated with control implementation, and modeling results in this regard can be of great utility for informing public policy decisions subject to budgetary constraints [2,3,4,5,12,14,16,25,26,42].…”

“…Given these constraints, mathematical models can serve as important tools for predicting the effects of control efforts and optimizing control efficacies and costs. Indeed, the efficacies of adult and larval control measure have been assessed and optimized using both simple, deterministic epidemic models [2,3,4,5] and complex disease models with features such as stochasticity [6,7], seasonality [8,9,10,11], host heterogeneity [11,12,13,14], and spatial structure [6,7,13].…”

“…To assess the effects and efficacy of real-world vector management strategies using a mathematical model, a modeler must first select a scheme by which the control's influence will be incorporated into the model's structure or behavior. One common choice is to simply infer the effects of control by analyzing changes in model behavior under variations in model parameters relative to their natural values [2,4,5,6,9,12,13,14,15,16,17,18,19]. For example, in many vector-borne disease models, the effects of adulticide on outbreak severity are inferred through the responses of important threshold quantities like the basic reproduction number [20,21] to increases in vector death rates, while the effects of larvicides are inferred through the analogous responses to increases in larval death rates or decreases in vector emergence rates [14,15,17,18].…”

“…Implicit controls, on the other hand, introduce no additional complexity into underlying disease models. The greater analytical tractability of implicit control facilitates model analysis, including the use of optimal control theory to predict potentially time-dependent variations in model parameters which optimally balance disease severity with control costs [2,4,5,12,14,25]. We emphasize that the sense of time-dependence for implicit control protocols is biologically distinct from the sense of time-dependence for explicit control protocols; implicit control's time-dependence is solely a reflection of changes in a controlling agency's implementation strategy (such as changes in application schedule or volume of pesticide released per application), while explicit control's time-dependence reflects changes in strategy as well as the biology and finite efficacy time of a control measure's interaction with a vector population.…”

Managing disease outbreaks: The importance of vector mobility and spatially heterogeneous control

“…Other models consider impulsive control protocols with finite natural efficacy times which are mathematically more complicated, but are also more realistic and more directly connected to real-world actionable control advice [19,22]. A few studies explore both approaches to control modeling [21,25]. In contrast, this paper utilizes a hybrid approach to control modeling introduced in Ref.…”