Limits...
Quantifying the impact of decay in bed-net efficacy on malaria transmission.

Ngonghala CN, Del Valle SY, Zhao R, Mohammed-Awel J - J. Theor. Biol. (2014)

Bottom Line: The potential impact of ITNs on reducing malaria transmission is limited due to inconsistent or improper use, as well as physical decay in effectiveness.We develop a model for malaria spread that captures the decrease in ITN effectiveness due to physical and chemical decay, as well as human behavior as a function of time.These analyses show that the basic reproduction number R0, and the infectious human population are most sensitive to bed-net coverage and the biting rate of mosquitoes.

View Article: PubMed Central - PubMed

Affiliation: Department of Global Health and Social Medicine, Harvard Medical School, Boston, MA 02115, USA; National Institute for Mathematical and Biological Synthesis, Knoxville, TN 37996-1527, USA. Electronic address: Calistus_Ngonghala@hms.harvard.edu.

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Graphical illustration of the dynamics of (a) bed-net efficacy, (b) mosquito biting rate, (c) bed-net efficacy due to mosquito mortality, and (d) mosquito mortality rate for the parameters: βmin = 0.01, βmax = 1.0, b0 = 0.53 (World Health Organization (WHO), 2012), T = 3 × 365, n = 6, μv0 = 1/14, and μv1 = 1/14. Figure (a) shows the protective power of ITNs. The effectiveness of the ITNs is high initially, but declines with time until the net is replaced or retreated. Figure (b) shows how the biting rate of mosquitoes is low soon after adoption of an ITN, but as the insecticide diminishes, the biting rate increases. Figures (c) and (d) show that as the effectiveness of mosquito nets declines with time, mosquito mortality due to ITN use also declines. For each of the figures, it is assumed that the useful life of ITNs is 3 years (WHO, 2011) and the dynamics are presented for 3650 days or 10 years.
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Figure 2: Graphical illustration of the dynamics of (a) bed-net efficacy, (b) mosquito biting rate, (c) bed-net efficacy due to mosquito mortality, and (d) mosquito mortality rate for the parameters: βmin = 0.01, βmax = 1.0, b0 = 0.53 (World Health Organization (WHO), 2012), T = 3 × 365, n = 6, μv0 = 1/14, and μv1 = 1/14. Figure (a) shows the protective power of ITNs. The effectiveness of the ITNs is high initially, but declines with time until the net is replaced or retreated. Figure (b) shows how the biting rate of mosquitoes is low soon after adoption of an ITN, but as the insecticide diminishes, the biting rate increases. Figures (c) and (d) show that as the effectiveness of mosquito nets declines with time, mosquito mortality due to ITN use also declines. For each of the figures, it is assumed that the useful life of ITNs is 3 years (WHO, 2011) and the dynamics are presented for 3650 days or 10 years.

Mentions: Bed-nets protect humans from mosquito bites and hence reduce the probability of malaria transmission. In addition to protecting humans who sleep under ITNs, they also offer some level of community-wide protection against malaria by killing adult mosquitoes, thereby reducing the available number of mosquitoes, which can bite humans (Killeen and Smith, 2007; Maxwell et al., 2002). Generally, the efficacy of LLINs is high when they are acquired and after being impregnated with insecticides, but decays over time. However, the protection level does not completely diminish since even without insecticide, nets act as physical barriers between mosquitoes and humans. Some studies have shown that untreated bed-nets offer about half the level of protection offered by ITNs against malaria (Clarke et al., 2001; WHO, 2007) and others have shown that they provide similar protection (Okumu et al., 2013). We assume that after ITNs have lost their insecticidal properties, they offer about half the same level of protection as new ITNs and the same level of protection as regular untreated nets. Also, we assume that all bed-nets are distributed and/or replaced at the same time. Although this is a simplifying assumption, it is a reasonable approximation towards quantifying the impact of replacing ITNs on malaria control. An appropriate functional form for the biting or contact rate of mosquitoes β(bβ(t)), must capture these important aspects. Thus, we model β(bβ(t)) through the following functional form: (2.2)β(bβ(t))=βmax-(βmax-βmin)bβ(t),bβ(t)=2n+12n+1(2n-12n+1+11+(tmodTT/2)n)b0, where n>1 is a dimensionless shape constant and T >0 is the useful life or duration of ITN efficacy. Observe that T can also represent the replacement or distribution period of ITNs. The parameter b0, for 0 ≤ b0 ≤ 1, captures the initial ITN coverage, where b0 = 0 represents no coverage and b0 = 1 depicts full coverage. This functional form for β captures the fact that regular untreated nets are half as efficient as ITNs; thus, limt→0+bβ(t) = b0 is the proportion of ITN usage in Agusto et al. (2013) and limt→T−bβ(t) = b0/2. See Fig. 2(a) and (b) for a graphical illustration of the dynamics of the time-dependent functions bβ and β.


Quantifying the impact of decay in bed-net efficacy on malaria transmission.

Ngonghala CN, Del Valle SY, Zhao R, Mohammed-Awel J - J. Theor. Biol. (2014)

Graphical illustration of the dynamics of (a) bed-net efficacy, (b) mosquito biting rate, (c) bed-net efficacy due to mosquito mortality, and (d) mosquito mortality rate for the parameters: βmin = 0.01, βmax = 1.0, b0 = 0.53 (World Health Organization (WHO), 2012), T = 3 × 365, n = 6, μv0 = 1/14, and μv1 = 1/14. Figure (a) shows the protective power of ITNs. The effectiveness of the ITNs is high initially, but declines with time until the net is replaced or retreated. Figure (b) shows how the biting rate of mosquitoes is low soon after adoption of an ITN, but as the insecticide diminishes, the biting rate increases. Figures (c) and (d) show that as the effectiveness of mosquito nets declines with time, mosquito mortality due to ITN use also declines. For each of the figures, it is assumed that the useful life of ITNs is 3 years (WHO, 2011) and the dynamics are presented for 3650 days or 10 years.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4374367&req=5

Figure 2: Graphical illustration of the dynamics of (a) bed-net efficacy, (b) mosquito biting rate, (c) bed-net efficacy due to mosquito mortality, and (d) mosquito mortality rate for the parameters: βmin = 0.01, βmax = 1.0, b0 = 0.53 (World Health Organization (WHO), 2012), T = 3 × 365, n = 6, μv0 = 1/14, and μv1 = 1/14. Figure (a) shows the protective power of ITNs. The effectiveness of the ITNs is high initially, but declines with time until the net is replaced or retreated. Figure (b) shows how the biting rate of mosquitoes is low soon after adoption of an ITN, but as the insecticide diminishes, the biting rate increases. Figures (c) and (d) show that as the effectiveness of mosquito nets declines with time, mosquito mortality due to ITN use also declines. For each of the figures, it is assumed that the useful life of ITNs is 3 years (WHO, 2011) and the dynamics are presented for 3650 days or 10 years.
Mentions: Bed-nets protect humans from mosquito bites and hence reduce the probability of malaria transmission. In addition to protecting humans who sleep under ITNs, they also offer some level of community-wide protection against malaria by killing adult mosquitoes, thereby reducing the available number of mosquitoes, which can bite humans (Killeen and Smith, 2007; Maxwell et al., 2002). Generally, the efficacy of LLINs is high when they are acquired and after being impregnated with insecticides, but decays over time. However, the protection level does not completely diminish since even without insecticide, nets act as physical barriers between mosquitoes and humans. Some studies have shown that untreated bed-nets offer about half the level of protection offered by ITNs against malaria (Clarke et al., 2001; WHO, 2007) and others have shown that they provide similar protection (Okumu et al., 2013). We assume that after ITNs have lost their insecticidal properties, they offer about half the same level of protection as new ITNs and the same level of protection as regular untreated nets. Also, we assume that all bed-nets are distributed and/or replaced at the same time. Although this is a simplifying assumption, it is a reasonable approximation towards quantifying the impact of replacing ITNs on malaria control. An appropriate functional form for the biting or contact rate of mosquitoes β(bβ(t)), must capture these important aspects. Thus, we model β(bβ(t)) through the following functional form: (2.2)β(bβ(t))=βmax-(βmax-βmin)bβ(t),bβ(t)=2n+12n+1(2n-12n+1+11+(tmodTT/2)n)b0, where n>1 is a dimensionless shape constant and T >0 is the useful life or duration of ITN efficacy. Observe that T can also represent the replacement or distribution period of ITNs. The parameter b0, for 0 ≤ b0 ≤ 1, captures the initial ITN coverage, where b0 = 0 represents no coverage and b0 = 1 depicts full coverage. This functional form for β captures the fact that regular untreated nets are half as efficient as ITNs; thus, limt→0+bβ(t) = b0 is the proportion of ITN usage in Agusto et al. (2013) and limt→T−bβ(t) = b0/2. See Fig. 2(a) and (b) for a graphical illustration of the dynamics of the time-dependent functions bβ and β.

Bottom Line: The potential impact of ITNs on reducing malaria transmission is limited due to inconsistent or improper use, as well as physical decay in effectiveness.We develop a model for malaria spread that captures the decrease in ITN effectiveness due to physical and chemical decay, as well as human behavior as a function of time.These analyses show that the basic reproduction number R0, and the infectious human population are most sensitive to bed-net coverage and the biting rate of mosquitoes.

View Article: PubMed Central - PubMed

Affiliation: Department of Global Health and Social Medicine, Harvard Medical School, Boston, MA 02115, USA; National Institute for Mathematical and Biological Synthesis, Knoxville, TN 37996-1527, USA. Electronic address: Calistus_Ngonghala@hms.harvard.edu.

Show MeSH
Related in: MedlinePlus