Insecticide-resistant mosquitoes and malaria control.

The emergence of insecticide-resistant mosquitoes strongly challenges the fight against mosquito-borne diseases, in particular malaria. In this paper, we formulate a system of nonlinear difference equations for malaria transmission cycle. Our model incorporates compartments for insecticide-resistant mosquitoes, where mutation is the only evolutionary force involved in the occurrence of resistant allele in the mosquito population. By deriving an epidemiological threshold, the global stability of the disease and the resistance-free fixed point is established for reduced recruitment rates of resistant mosquitoes. Furthermore, by employing numerical techniques, we showed that the mosquito-human transmission cycle of malaria and its prevalence could be impacted by mutation rate, the personal protection of hosts and the density of mosquitoes. Our results highlight that given a large mosquito population, the presence of even a small number of resistant mosquitoes to an insecticide could make the insecticide ineffective for malaria control. This suggests the need for effective insecticide management strategy, alternate mosquito control approaches, educating the public about personal protection and reduction of mosquito population in a given environment.

The impact of bed-net use on malaria prevalence.

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 R 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 R. 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.

Backward bifurcation and optimal control in transmission dynamics of west nile virus.

The paper considers a deterministic model for the transmission dynamics of West Nile virus (WNV) in the mosquito-bird-human zoonotic cycle. The model, which incorporates density-dependent contact rates between the mosquito population and the hosts (birds and humans), is rigorously analyzed using dynamical systems techniques and theories. These analyses reveal the existence of the phenomenon of backward bifurcation (where the stable disease-free equilibrium of the model co-exists with a stable endemic equilibrium when the reproduction number of the disease is less than unity) in WNV transmission dynamics. The epidemiological consequence of backward bifurcation is that the classical requirement of having the reproduction number less than unity, while necessary, is no longer sufficient for WNV elimination from the population. It is further shown that the model with constant contact rates can also exhibit this phenomenon if the WNV-induced mortality in the avian population is high enough. The model is extended to assess the impact of some anti-WNV control measures, by re-formulating the model as an optimal control problem with density-dependent demographic parameters. This entails the use of two control functions, one for mosquito-reduction strategies and the other for personal (human) protection, and redefining the demographic parameters as density-dependent rates. Appropriate optimal control methods are used to characterize the optimal levels of the two controls. Numerical simulations of the optimal control problem, using a set of reasonable parameter values, suggest that mosquito reduction controls should be emphasized ahead of personal protection measures.