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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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The basic reproduction number of model (2.4) for βmax∈{0.5, 1.0} as a function of ITN coverage, b0. Solid blue lines show the basic reproduction number , for time-dependent periodic bj, dashed green lines denote the basic reproduction number , for time-averaged bj, where j∈{β, μv}, and dash-dotted red lines denote the basic reproduction number R0, for bβ = bμv = b0. Figure (a) indicates that ITN alone may be enough to control malaria, while figure (b) indicates that ITN alone might not be enough to control malaria, if ITN efficacy declines over time. The horizontal line denoted by  represents a basic reproduction number of value unity. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
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Figure 5: The basic reproduction number of model (2.4) for βmax∈{0.5, 1.0} as a function of ITN coverage, b0. Solid blue lines show the basic reproduction number , for time-dependent periodic bj, dashed green lines denote the basic reproduction number , for time-averaged bj, where j∈{β, μv}, and dash-dotted red lines denote the basic reproduction number R0, for bβ = bμv = b0. Figure (a) indicates that ITN alone may be enough to control malaria, while figure (b) indicates that ITN alone might not be enough to control malaria, if ITN efficacy declines over time. The horizontal line denoted by represents a basic reproduction number of value unity. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)

Mentions: We investigate the relationship between the basic reproduction number of the periodic malaria transmission model (2.4) and the initial ITN coverage b0 for different values of the maximum biting rate, βmax and the lifespan of ITNs, T. We consider the dynamics of three basic reproduction numbers, R0, and corresponding to bβ = bμv = b0, a time-averaged bj, i.e., , and time-dependent periodic bj, respectively, where j∈{β, μv}. R0 and can be computed using the next generation matrix approach, while can be computed using the algorithm outlined in Section 4.2. In order to determine which of these thresholds estimates disease transmission risk better, we plot the dynamics of each of them as a function of the initial ITN coverage b0 for βmax∈{0.5, 1.0} and n=6, while keeping all the other parameters as presented in Table 1. Fig. 5 illustrates the dynamics of the basic reproduction number of our model as a function of b0 for the three case-scenarios. Fig. 5(a) shows the dynamics of the three basic reproduction numbers for βmax = 0.5. We can infer from the figure that R0 and underestimate the disease transmission risk for 0.24≤b0≤0.6 and 0.5≤b0≤0.6, respectively. This shows that for bβ = bμv = b0, about 24% ITN coverage might be required to contain malaria; for bj = [bj], j∈{β, μv}, about 50% coverage might be required to bring malaria under control; while for the time-dependent periodic case, about 60% ITN cover-age might be required to contain malaria. The first case might be reasonable in areas of extremely low malaria prevalence, however, it is probably not applicable in malaria endemic regions. The cases for and seem to be realistic for malaria endemic areas. Based on the conclusions in Killeen et al. (2007), a 60% personal coverage will result in an equitable community-wide protection. This result confirms the importance of capturing the fact that ITN efficacy declines over time when developing models for malaria transmission. Fig. 5(b) shows that about 51% ITN coverage might be required to control malaria when βmax = 1. In this case, R0<1 for 0.51≤b0≤1. However, and are always greater than one, illustrating that in areas of hyper-endemic malaria, where mosquitoes can easily bite humans, ITNs alone may not be sufficient to control malaria. In such a situation, ITNs must be combined with other malaria control measures to reduce disease spread.


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)

The basic reproduction number of model (2.4) for βmax∈{0.5, 1.0} as a function of ITN coverage, b0. Solid blue lines show the basic reproduction number , for time-dependent periodic bj, dashed green lines denote the basic reproduction number , for time-averaged bj, where j∈{β, μv}, and dash-dotted red lines denote the basic reproduction number R0, for bβ = bμv = b0. Figure (a) indicates that ITN alone may be enough to control malaria, while figure (b) indicates that ITN alone might not be enough to control malaria, if ITN efficacy declines over time. The horizontal line denoted by  represents a basic reproduction number of value unity. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 5: The basic reproduction number of model (2.4) for βmax∈{0.5, 1.0} as a function of ITN coverage, b0. Solid blue lines show the basic reproduction number , for time-dependent periodic bj, dashed green lines denote the basic reproduction number , for time-averaged bj, where j∈{β, μv}, and dash-dotted red lines denote the basic reproduction number R0, for bβ = bμv = b0. Figure (a) indicates that ITN alone may be enough to control malaria, while figure (b) indicates that ITN alone might not be enough to control malaria, if ITN efficacy declines over time. The horizontal line denoted by represents a basic reproduction number of value unity. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
Mentions: We investigate the relationship between the basic reproduction number of the periodic malaria transmission model (2.4) and the initial ITN coverage b0 for different values of the maximum biting rate, βmax and the lifespan of ITNs, T. We consider the dynamics of three basic reproduction numbers, R0, and corresponding to bβ = bμv = b0, a time-averaged bj, i.e., , and time-dependent periodic bj, respectively, where j∈{β, μv}. R0 and can be computed using the next generation matrix approach, while can be computed using the algorithm outlined in Section 4.2. In order to determine which of these thresholds estimates disease transmission risk better, we plot the dynamics of each of them as a function of the initial ITN coverage b0 for βmax∈{0.5, 1.0} and n=6, while keeping all the other parameters as presented in Table 1. Fig. 5 illustrates the dynamics of the basic reproduction number of our model as a function of b0 for the three case-scenarios. Fig. 5(a) shows the dynamics of the three basic reproduction numbers for βmax = 0.5. We can infer from the figure that R0 and underestimate the disease transmission risk for 0.24≤b0≤0.6 and 0.5≤b0≤0.6, respectively. This shows that for bβ = bμv = b0, about 24% ITN coverage might be required to contain malaria; for bj = [bj], j∈{β, μv}, about 50% coverage might be required to bring malaria under control; while for the time-dependent periodic case, about 60% ITN cover-age might be required to contain malaria. The first case might be reasonable in areas of extremely low malaria prevalence, however, it is probably not applicable in malaria endemic regions. The cases for and seem to be realistic for malaria endemic areas. Based on the conclusions in Killeen et al. (2007), a 60% personal coverage will result in an equitable community-wide protection. This result confirms the importance of capturing the fact that ITN efficacy declines over time when developing models for malaria transmission. Fig. 5(b) shows that about 51% ITN coverage might be required to control malaria when βmax = 1. In this case, R0<1 for 0.51≤b0≤1. However, and are always greater than one, illustrating that in areas of hyper-endemic malaria, where mosquitoes can easily bite humans, ITNs alone may not be sufficient to control malaria. In such a situation, ITNs must be combined with other malaria control measures to reduce disease spread.

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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Related in: MedlinePlus