We use a time dependent modification of the Kermack and McKendrick model to study the evolution of the influenza A(H1N1)v epidemic reported in the Mexico City area under the control measures used during April and May 2009. The model illustrates how the sanitary measures postponed the peak of the epidemic and decreased its intensity. It provides quantitative predictions on the effect of relaxing the sanitary measures after a period of control. We show how the sanitary measures reduced the maximal prevalence of the infected population from 10% to less than 6% of the total population. We also show how the model predicts the time of maximal prevalence and explains the effect of the control measures.

In this paper, we analyse the interaction of different species of birds and mosquitoes on the dynamics of West Nile virus (WNV) infection. We study the different transmission efficiencies of the vectors and birds and the impact on the possible outbreaks. We show that the basic reproductive number is the weighted mean of the basic reproductive number of each species, weighted by the relative abundance of its population in the location. These results suggest a possible explanation of why there are no outbreaks of WNV in Mexico.

The evolution of lump solutions for the Zakharov-Kuznetsov equation and the surface electromigration equation, which describes mass transport along the surface of nanoconductors, is studied. Approximate equations are developed for these equations, these approximate equations including the important effect of the dispersive radiation shed by the lumps as they evolve. The approximate equations show that lumplike initial conditions evolve into lump soliton solutions for both the Zakharov-Kuznetsov equation and the surface electromigration equations. Solutions of the approximate equations, within their range of applicability, are found to be in good agreement with full numerical solutions of the governing equations. The asymptotic and numerical results predict that localized disturbances will always evolve into nanosolitons. Finally, it is found that dispersive radiation plays a more dominant role in the evolution of lumps for the electromigration equations than for the Zakharov-Kuznetsov equation.