The impact of bed-net use on malaria prevalence

Abstract

Malaria infection continues to be a major problem in many parts of the world including the Americas, Asia, and Africa. Insecticide-treated bed-nets have shown to reduce malaria cases by 50%; however, improper handling and human behavior can diminish their effectiveness. We formulate and analyze a mathematical model that considers the transmission dynamics of malaria infection in mosquito and human populations and investigate the impact of bed-nets on its control. The effective reproduction number is derived and existence of backward bifurcation is presented. The backward bifurcation implies that the reduction of scriptR below unity alone is not enough to eradicate malaria, except when the initial cases of infection in both populations are small. Our analysis demonstrate that bed-net usage has a positive impact in reducing the reproduction number scriptR. The results show that if 75% of the population were to use bed-nets, malaria could be eliminated. We conclude that more data on the impact of human and mosquito behavior on malaria spread is needed to develop more realistic models and better predictions.

Analysis of a malaria model with mosquito host choice and bed-net control

“…which was found in [1]. Being b crit > b 1 , for π > 1, it can be deduced that this 255 critical value of bed-net usage increases when the mosquitoes preference for biting 256 infected humans is taken into account.…”

“…Therefore the role of b in the model is to reduce the contact rate 106 β and to increase the mosquito death rate η. Therefore, it is assumed that [1] 107…”

“…Denote by E * = (S * h , I * h , S * v , I * v ) a generic endemic equilibrium of model (1). In view of (1), the components must be solutions of the following equations:…”

“…However, the assumption of a constant total population (vector or humans) 216 allows to reduce model (1) to a more tractable three-dimensional system. In order 217 to avoid the restriction α = 0, we assume that the total population at equilibrium 218 is that of vectors, instead of humans, as done in [1], i. e. we assume N v (t) = V 219 (const. ), for all t > 0.…”

“…The baseline model used here is the vector-bias malaria model considered in [7], 288 which has been extended by adopting the bed-net usage modeling proposed in [1].…”