Dynamic modelling of personal protection control strategies for vector-borne disease limits the role of diversity amplification

Abstract

Personal protection measures, such as bed nets and repellents, are important tools for the suppression of vector-borne diseases like malaria and Zika, and the ability of health agencies to distribute protection and encourage its use plays an important role in the efficacy of community-wide disease management strategies. Recent modelling studies have shown that a counterintuitive diversity-driven amplification in community-wide disease levels can result from a population's partial adoption of personal protection measures, potentially to the detriment of disease management efforts. This finding, however, may overestimate the negative impact of partial personal protection as a result of implicit restrictive model assumptions regarding host compliance, access to and longevity of protection measures. We establish a new modelling methodology for incorporating community-wide personal protection distribution programmes in vector-borne disease systems which flexibly accounts for compliance, access, longevity and control strategies by way of a flow between protected and unprotected populations. Our methodology yields large reductions in the severity and occurrence of amplification effects as compared to existing models.

Keywords: bed nets; diversity amplification; epidemiological control; insect repellent; personal protection; vector-borne disease.

Figure 1.

Dependencies of on DEET (1/γ = 15 days) control strength for the dynamic two-class model (blue), static two-class model (red) and one-class model (green). Corresponding equilibrium proportions of protected hosts are given by the dashed black curve. Two-host models display diversity amplification at control strengths where respective scaled curves rise above the grey line. Large suppressions in amplification severity and occurrence range are indicated by vertical and horizontal purple arrows, respectively, in (d). (a) Density-dependent infection AN_h = 0.1 d⁻¹, (b) moderate infection AN_h = 1.0 d⁻¹, (c) frequency-dependent infection AN_h = 10.0 d⁻¹ and (d) frequency-dependent infection (wide view).

Figure 2.

Dependencies of on intermediate protection (1/γ = 9 months) control strength for the dynamic two-class model (blue), static two-class model (red) and one-class model (green). Corresponding equilibrium proportions of protected hosts are given by the dashed black curve. Large suppressions in amplification severity and occurrence range are indicated by vertical and horizontal purple arrows, respectively, in (d). (a) Density-dependent infection AN_h = 0.1 d⁻¹, (b) moderate infection AN_h = 1.0 d⁻¹, (c) frequency-dependent infection AN_h = 10.0 d⁻¹ and (d) frequency-dependent infection (wide view).

Figure 3.

Dependencies of on bed net (1/γ = 5 years) control strength for the dynamic two-class model (blue), static two-class model (red) and one-class model (green). Corresponding equilibrium proportions of protected hosts are given by the dashed black curve. Suppressions in amplification severity and occurrence range are indicated by vertical and horizontal purple arrows, respectively, in (d). (a) Density-dependent infection AN_h = 0.1 d⁻¹, (b) moderate infection AN_h = 1.0 d⁻¹, (c) frequency-dependent infection AN_h = 10.0 and (d) frequency-dependent infection (wide view).

Figure 4.

Illustrations of amplification range and strength reduction as functions of AN_h using the dynamic two-class model (blue), static two-class model (red) and one-class model (green). The minimum control strength for amplification suppression is the value of control strength κ* such that scaled exceeds unity for all control strengths κ ∈ [0, κ*]. The maximum scaled is the value of scaled at the peak of a model's versus κ curve for a given value of AN_h. (a) Amplifaction range reduction 1/γ = 15 days, (b) amplifaction severity reduction 1/γ = 15 days, (c) amplifaction range reduction 1/γ = 9 months, (d) amplifaction severity reduction 1/γ = 9 months, (e) amplifaction range reduction 1/γ = 5 years and (f) amplifaction severity reduction 1/γ = 5 years.