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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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Numerical solutions of system (2.4) for b∈{20, 0.70, 0.75} and the other parameters in Table 1. The initial conditions used are . Graphs (a) and (d) show stable disease-free human and mosquito equilibrium solutions. Graphs (b) and (c) show stable endemic human equilibrium solutions, while graphs (e) and (f) show stable endemic mosquito equilibrium solutions.
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Figure 4: Numerical solutions of system (2.4) for b∈{20, 0.70, 0.75} and the other parameters in Table 1. The initial conditions used are . Graphs (a) and (d) show stable disease-free human and mosquito equilibrium solutions. Graphs (b) and (c) show stable endemic human equilibrium solutions, while graphs (e) and (f) show stable endemic mosquito equilibrium solutions.

Mentions: Fig. 4 shows the dynamics of system (2.4) for γ̃h = 1/30, ρh = 9 × 10−3, the other parameters in Table 1 and b∈{0.20, 0.70, 0.75}. For b = 0.75, R0 = 0.97<1, and the system approaches the disease-free equilibrium solution over time (Fig. 4(a) and (d)). This represents the situation in which 75% ITN coverage is successful in containing the malaria disease. For b = 0.70, R0 = 1.20>1 and the system approaches the endemic equilibrium solution over time (Fig. 4(b) and (e)). This depicts the situation in which 70% ITN coverage is unsuccessful in containing the malaria disease. For b = 0.2, R0 = 4.83>1 and the system converges to the endemic equilibrium solution (Fig. 4(c) and (f)). In this case, the disease persists due to inadequate ITN coverage. This numerical solution agrees with the analytical result presented in Theorem 3.2.


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)

Numerical solutions of system (2.4) for b∈{20, 0.70, 0.75} and the other parameters in Table 1. The initial conditions used are . Graphs (a) and (d) show stable disease-free human and mosquito equilibrium solutions. Graphs (b) and (c) show stable endemic human equilibrium solutions, while graphs (e) and (f) show stable endemic mosquito equilibrium solutions.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 4: Numerical solutions of system (2.4) for b∈{20, 0.70, 0.75} and the other parameters in Table 1. The initial conditions used are . Graphs (a) and (d) show stable disease-free human and mosquito equilibrium solutions. Graphs (b) and (c) show stable endemic human equilibrium solutions, while graphs (e) and (f) show stable endemic mosquito equilibrium solutions.
Mentions: Fig. 4 shows the dynamics of system (2.4) for γ̃h = 1/30, ρh = 9 × 10−3, the other parameters in Table 1 and b∈{0.20, 0.70, 0.75}. For b = 0.75, R0 = 0.97<1, and the system approaches the disease-free equilibrium solution over time (Fig. 4(a) and (d)). This represents the situation in which 75% ITN coverage is successful in containing the malaria disease. For b = 0.70, R0 = 1.20>1 and the system approaches the endemic equilibrium solution over time (Fig. 4(b) and (e)). This depicts the situation in which 70% ITN coverage is unsuccessful in containing the malaria disease. For b = 0.2, R0 = 4.83>1 and the system converges to the endemic equilibrium solution (Fig. 4(c) and (f)). In this case, the disease persists due to inadequate ITN coverage. This numerical solution agrees with the analytical result presented in Theorem 3.2.

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