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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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Simulation results showing the long-term dynamics of the mosquito population in the non-autonomous model (2.4) for different values of b0 and βmax. The initial conditions used are . The disease dies out for b0 = 0.6 and βmax = 0.5 (Graph (a)) and persists when b0 = 0.1 and βmax =0.5 (Graph (b)) and when b0 = 1.0 and βmax = 1.0 (Graph (c)).
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Figure 8: Simulation results showing the long-term dynamics of the mosquito population in the non-autonomous model (2.4) for different values of b0 and βmax. The initial conditions used are . The disease dies out for b0 = 0.6 and βmax = 0.5 (Graph (a)) and persists when b0 = 0.1 and βmax =0.5 (Graph (b)) and when b0 = 1.0 and βmax = 1.0 (Graph (c)).

Mentions: We now illustrate the dynamics of the full non-autonomous model system when R0<1 and for two cases in which R0>1. The case in which R0<1 is attained with an initial ITN coverage of b0 = 0.6 and a maximum mosquito-biting rate of βmax = 0.5, while the cases for which R0>1 are obtained by with the respective bed-net coverage and maximum biting rate pairs (b0 = 0.1, βmax = 0.5) and (b0 = 1.0, βmax = 1.0). Figs. 7 and 8 show numerical simulations of system (2.4) for the baseline parameters in Table 1, different values of the initial ITN coverage b0, and the maximum mosquito-biting rate βmax. The top row of Fig. 7, i.e., Fig. 7(a)–(c) show transient dynamics of the human population, while the bottom row of Fig. 7, i.e., Fig. 7(d)–(f) show the long-term asymptotic dynamics of the human population. Fig. 7(a) and (d) indicate that the disease dies out when b0 = 0.6 and βmax = 0.5, since this parameter regime generates a basic reproduction number that is less than one. Fig. 7(b) and (e) show that the disease establishes itself in the population for a low initial ITN coverage of b0 = 0.1 and βmax = 0.5, since this parameter set gives a basic reproduction number that is bigger than one. Fig. 7(c) and (f) depict the dynamics when both b0, and βmax, are high. For example, when b0 = 1.0 and βmax = 1.0, the disease persists in the population. That is, in areas in which mosquitoes bite humans frequently, the disease persist irrespective of the level of ITN coverage. This implies that in highly endemic areas, ITNs might not be enough to control malaria transmission. Thus, areas with high malaria prevalence might need other interventions such as indoor residual spraying, intermittent preventive treatment, and artemisinin-based combination therapies to control the infection. The corresponding long-term dynamics of the mosquito population are illustrated in Fig. 8. The long-term dynamics illustrated in Figs. 7–8 depict bounded periodic oscillations, which are due to the forcing introduced by the time-periodic parameters bβ and bμv.


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)

Simulation results showing the long-term dynamics of the mosquito population in the non-autonomous model (2.4) for different values of b0 and βmax. The initial conditions used are . The disease dies out for b0 = 0.6 and βmax = 0.5 (Graph (a)) and persists when b0 = 0.1 and βmax =0.5 (Graph (b)) and when b0 = 1.0 and βmax = 1.0 (Graph (c)).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 8: Simulation results showing the long-term dynamics of the mosquito population in the non-autonomous model (2.4) for different values of b0 and βmax. The initial conditions used are . The disease dies out for b0 = 0.6 and βmax = 0.5 (Graph (a)) and persists when b0 = 0.1 and βmax =0.5 (Graph (b)) and when b0 = 1.0 and βmax = 1.0 (Graph (c)).
Mentions: We now illustrate the dynamics of the full non-autonomous model system when R0<1 and for two cases in which R0>1. The case in which R0<1 is attained with an initial ITN coverage of b0 = 0.6 and a maximum mosquito-biting rate of βmax = 0.5, while the cases for which R0>1 are obtained by with the respective bed-net coverage and maximum biting rate pairs (b0 = 0.1, βmax = 0.5) and (b0 = 1.0, βmax = 1.0). Figs. 7 and 8 show numerical simulations of system (2.4) for the baseline parameters in Table 1, different values of the initial ITN coverage b0, and the maximum mosquito-biting rate βmax. The top row of Fig. 7, i.e., Fig. 7(a)–(c) show transient dynamics of the human population, while the bottom row of Fig. 7, i.e., Fig. 7(d)–(f) show the long-term asymptotic dynamics of the human population. Fig. 7(a) and (d) indicate that the disease dies out when b0 = 0.6 and βmax = 0.5, since this parameter regime generates a basic reproduction number that is less than one. Fig. 7(b) and (e) show that the disease establishes itself in the population for a low initial ITN coverage of b0 = 0.1 and βmax = 0.5, since this parameter set gives a basic reproduction number that is bigger than one. Fig. 7(c) and (f) depict the dynamics when both b0, and βmax, are high. For example, when b0 = 1.0 and βmax = 1.0, the disease persists in the population. That is, in areas in which mosquitoes bite humans frequently, the disease persist irrespective of the level of ITN coverage. This implies that in highly endemic areas, ITNs might not be enough to control malaria transmission. Thus, areas with high malaria prevalence might need other interventions such as indoor residual spraying, intermittent preventive treatment, and artemisinin-based combination therapies to control the infection. The corresponding long-term dynamics of the mosquito population are illustrated in Fig. 8. The long-term dynamics illustrated in Figs. 7–8 depict bounded periodic oscillations, which are due to the forcing introduced by the time-periodic parameters bβ and bμv.

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