Modeling the Dynamics of Malaria Transmission with Bed Net Protection Perspective

Abstract

We propose and analyze an epidemiological model to evaluate the effectiveness of bed nets as a prophylactic measure in malaria-endemic areas. The main purpose in this work is the modeling of the aggressiveness of anopheles mosquitoes relative to the way humans use to protect themselves against bites of mosquitoes. This model is a system of several differential equations: the number of equations depends on the particular assumptions of the model. We compute the basic reproduction number 0  , and show that if 0 1  ≤ , the disease free equilibrium (DFE) is globally asymptotically stable on the non-negative orthant. If 0 > 1  , the system admits a unique endemic equilibrium (EE) that is globally and asymptotically stable. Numerical simulations are presented corresponding to scenarios typical of malaria-endemic areas, based on data collected in the literature. Finally, we discuss the relative effectiveness of different kinds of bed nets.

Global Sensitivity Analysis to Study the Impacts of Bed-Nets, Drug Treatment, and Their Efficacies on a Two-Strain Malaria Model

“…These changes are attributed to wide-scale deployment of malaria control strategies. These include the use of conventional insecticide-treated bed-nets (ITNs), long-lasting insecticide nets (LLINs), intermittent preventive treatment (IPT) especially for pregnant women during the anti-natal period, reducing mosquito population through the destruction of breeding sites or killing of the larva stage at breading sites that cannot be destroyed, indoor residual spraying (IRS), and the use of the sterile insect technique [2][3][4][5][6][7][8]. Despite the remarkable progress, malaria remains a major cause of mortality and morbidity in many parts of the world.…”

“…One key constraint in sustainable use of ITNs is the need for regular re-treatment, otherwise they lose their efficiencies. In the models reported in [4,50], the authors introduced an explicit equation for mosquito biting rates as a linear decreasing function of the proportion of ITN usage. Although this a plausible approach, the biting rate function does not contain a parameter that will mimic the efficacy of ITNs.…”

Analysis of Malaria Control Measures’ Effectiveness Using Multistage Vector Model

“…On the entire set (R >0 ) u and for each i, given that ( . On the other hand, when (I i − I i )(I q − I q ) ≤ 0 we may show h 1 (x) ≤ 0, h 2 (x) ≤ 0 and p 1 i (x) ≤ 0 by applying the same corollary to the following data (given in pairs as (number, weight)) In view of expressions (20), (21) for G 1 i and expressions (23), (24) for G 2 i , the results of the previous paragraph show that G k i ≤ 0 on the entire set (R >0 ) u for k ∈ {1, 2}. Since we have also shown that f k (x) ≤ 0 on Ω k for k ∈ {1, 2}, in view of expressions (19) and (22) for dV ee d t (x(t)) we may conclude that dV ee d t (x(t)) ≤ 0 for all x(t) ∈ (R >0 ) u .…”

“…Adult mosquitoes alternate between two activities: questing (that is, seeking a host to bite for a blood meal) and resting (to lay down eggs, or to digest a blood meal). In [21] it was assumed that all susceptible mosquitoes are in the questing state-the current model improves on this by introducing an additional compartment for susceptible mosquitoes in the resting state that have successfully obtained blood meal(s) and are not yet infected.…”

“…This inclusion is justified, since malaria is a major cause of death in endemic areas. As in [21], we omit Exposed and Removed classes for hosts: the duration of Exposed and Removed states can be assumed to be negligible due to the high density of anopheles mosquitoes on the one hand, and rapid detection and treatment of infectious individuals on the other hand. Results for more sophisticated models that include Exposed and/or Removed state(s) are reserved for forthcoming papers.…”