Recasting the theory of mosquito-borne pathogen transmission dynamics and control

Abstract

Mosquito-borne diseases pose some of the greatest challenges in public health, especially in tropical and sub-tropical regions of the world. Efforts to control these diseases have been underpinned by a theoretical framework developed for malaria by Ross and Macdonald, including models, metrics for measuring transmission, and theory of control that identifies key vulnerabilities in the transmission cycle. That framework, especially Macdonald's formula for R0 and its entomological derivative, vectorial capacity, are now used to study dynamics and design interventions for many mosquito-borne diseases. A systematic review of 388 models published between 1970 and 2010 found that the vast majority adopted the Ross-Macdonald assumption of homogeneous transmission in a well-mixed population. Studies comparing models and data question these assumptions and point to the capacity to model heterogeneous, focal transmission as the most important but relatively unexplored component in current theory. Fine-scale heterogeneity causes transmission dynamics to be nonlinear, and poses problems for modeling, epidemiology and measurement. Novel mathematical approaches show how heterogeneity arises from the biology and the landscape on which the processes of mosquito biting and pathogen transmission unfold. Emerging theory focuses attention on the ecological and social context for mosquito blood feeding, the movement of both hosts and mosquitoes, and the relevant spatial scales for measuring transmission and for modeling dynamics and control.

Keywords: Dengue; Filariasis; Malaria; Mosquito-borne pathogen transmission; Vector control; West Nile virus.

Figure 1.

The central and unifying concepts emerging from the Ross–Macdonald model were vectorial capacity and R₀. Vectorial capacity, denoted v also called the ‘daily reproductive rate’, describes the intensity of transmission by mosquitoes, the number of infectious bites that would eventually arise from all the mosquitoes that bite a single human on a single day under a set of simplifying assumptions that are both parsimonious and mathematically convenient: the ratio of mosquitoes to vertebrate hosts (m) is assumed to be constant; mosquitoes are assumed to feed and die at a constant per-capita rate (f and g, respectively), to take a constant portion of their bloodmeals on the pathogen's host (Q), and to have a constant latent period (v). These ‘atomic’ parameters can be combined into three terms that have natural interpretations in the field: the number of mosquitoes biting a person in a day (mfQ, for human malaria, which is the human biting rate), the probability a mosquito survives through the latent period (e^−gv), and the expected number of bites on the pathogen's host given by an infectious mosquito (fQ/g). The product of these quantities is vectorial capacity: V = mfQ²e^−gv/g. The basic reproductive number, R₀ sums the daily reproductive output of the pathogen, discounted by the inefficient transmission from infectious mosquitoes to susceptible hosts (b) or vice versa (c), for as long as many days as a host remains infectious (1/r): the formula is R₀ = bVc/r. Note: vectorial capacity assumes c = 1. Transmission in the populations of mosquitoes and hosts assumed mass-action kinetics, like two chemical species interacting in a chemostat, so location was vaguely defined, populations are large relative to R₀, biting risk is evenly distributed and redistributed on each blood meal. Most models developed since 1970 continue to adopt most of these assumptions.

Figure 2.

A richer body of theory has been developed since 1970 by elaborating upon the parsimonious assumptions of the Ross–Macdonald model, to include some of the features illustrated here. An important question has been the causes and dynamic consequences of fluctuating mosquito populations over time and space. In some cases, models have coupled adult egg laying with models of aquatic mosquito ecology (blue, at left), including some models that explicitly consider the abiotic and biotic factors that regulate mosquito populations. Other models have considered other aspects of the mosquito feeding cycle, including oviposition behavior and mosquito movement. Other models have expanded on the concepts relating to mixing behavior with models of host selection, heterogeneous biting, or spatial dynamics (red). Some of the greatest differences occur in the expanded models of pathogen infections in hosts, which differ in important ways for malaria, filariasis, and arboviral infections. Despite the rich body of theory that is available, most models continue to adopt the Ross–Macdonald assumptions by default: most models differ from the Ross–Macdonald model in fewer than two key assumptions.

Figure 3.

Recasting the theory of transmission requires examination of the factors that give rise to new infections and allow a pathogen to persist. This requires an explicit consideration of the spatial scales that characterize transmission. Existing mathematical theory for transmission of a pathogen by mosquitos focuses on the blood meal itself and factors that affect intensity of transmission (1). New mathematical theory must consider the broader ecological and epidemiological context that determines where and when key encounters between mosquitoes and vertebrate hosts occur. After emerging from aquatic habitats or after laying eggs (2), mosquitoes search for the kinds of habitats where blood feeding typically occurs, such as inside human dwellings (3). Behavioral and physical attributes of mosquitoes and vertebrate hosts, as well as various kinds of vector control strategies (4) determine the outcome of an encounter at mosquito feeding habitats; i.e. a successful blood meal on a particular host, mosquito death or an unsuccessful attempt to feed. Heterogeneity in biting risk among various mosquito blood-feeding habitats depends on mosquito movement (5) and on patterns of human movement (6). The direction of movement among feeding habitats by infected (red) or uninfected (blue) vertebrate hosts (6) and the relative allocation of a host's time at those locations (3, 6) determine the spatial scale of pathogen transmission by hosts. Likewise, alternating mosquito movement between blood-feeding and egg-laying habitats (2) determines the extent of pathogen movement by mosquitoes. At larger spatial scales (7), dispersal of mosquitoes by wind or as cargo and long-distance travel by vertebrate hosts for vacation, business travel, seasonal migration, and other factors determine how the pathogens disperse and persist locally, regionally and globally.