Quantifying the impact of decay in bed-net efficacy on malaria transmission.
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.
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
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Mentions: We now illustrate numerically the existence and stability of endemic equilibria and the occurrence of a backward bifurcation for system (2.4). Unless otherwise stated here and in subsequent sections, the parameters used in our simulations are the baseline parameters provided in Table 1. Fig. 3 illustrates the dynamics of system (2.4) for γ̃h = 1/30, ρh = 9 × 10−3 and within parameter regimes determined by the human disease-induced mortality rate δh, where a forward or a backward bifurcation occurs. Apart from the fact that a higher value of δh might be required for a backward bifurcation, the same qualitative results are obtained with the baseline values of γ̃h and ρh. Fig. 3(a) shows a forward bifurcation, wherein a stable disease-free equilibrium solution exists when R0 <1 and a stable endemic equilibrium solution exists when R0 >1. Fig. 3(b) shows a barely noticeable backward bifurcation when . Figure 3(c) indicates that for , there is an asymptotically stable disease-free equilibrium solution Edf and for , there is a backward bifurcation. This result implies that a locally stable disease-free equilibrium solution coexists with a locally stable endemic equilibrium and an unstable endemic equilibrium. These results confirm Theorems 3.2 and 3.3.
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.