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.

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.

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.