Every year, influenza causes high morbidity and mortality especially among the immunocompromised persons worldwide. The emergence of drug resistance has been a major challenge in curbing the spread of influenza. In this paper, a mathematical model is formulated and used to analyze the transmission dynamics of influenza A virus having incorporated the aspect of drug resistance. The qualitative analysis of the model is given in terms of the control reproduction number,Rc. The model equilibria are computed and stability analysis carried out. The model is found to exhibit backward bifurcation prompting the need to lowerRcto a critical valueRc∗for effective disease control. Sensitivity analysis results reveal that vaccine efficacy is the parameter with the most control over the spread of influenza. Numerical simulations reveal that despite vaccination reducing the reproduction number below unity, influenza still persists in the population. Hence, it is essential, in addition to vaccination, to apply other strategies to curb the spread of influenza.

A deterministic SEIR model of rift valley fever (RVF) with climate change parameters was considered to compute the basic reproduction numberℛ0and investigate the impact of temperature and precipitation onℛ0. To study the effect of model parameters toℛ0, sensitivity and elasticity analysis ofℛ0were performed. When temperature and precipitation effects are not considered,ℛ0is more sensitive to the expected number of infectedAedesspp. due to one infected livestock and more elastic to the expected number of infected livestock due to one infectedAedesspp. When climatic data are used,ℛ0is found to be more sensitive and elastic to the expected number of infected eggs laid byAedesspp. via transovarial transmission, followed by the expected number of infected livestock due to one infectedAedesspp. and the expected number of infectedAedesspp. due to one infected livestock for both regions Arusha and Dodoma. These results call for attention to parameters regarding incubation period, the adequate contact rate ofAedesspp. and livestock, the infective periods of livestock andAedesspp., and the vertical transmission inAedesspecies.