We present new mathematical models that include the impact of using selected preventative measures such as insecticide treated nets (ITN) in controlling or ameliorating the spread of the Zika virus. For these models, we derive the basic reproduction number and sharp estimates for the final size relation. We first present a single-stage model which is later extended to a new multistage model for Zika that incorporates more realistic incubation stages for both the humans and vectors. For each of these models, we derive a basic reproduction number and a final size relation estimate. We observe that the basic reproduction number for the multistage model converges to expected values for a standard Zika epidemic model with fixed incubation periods in both hosts and vectors. Finally, we also perform several computational experiments to validate the theoretical results obtained in this work and study the influence of various parameters on the models.
Youth that live in public housing communities with high social and financial needs are at risk of getting involved in illegal drug trafficking gangs that are controlled by adults. This social disease spreads like an epidemic in these densely populated sectors and metropolitan area. In this work, a model based on SIR disease dynamics is used to study the spread of gangs in vulnerable youth and adult sub-populations. Three types of mixing patterns govern interaction between the groups: proportionate, preferred and like-with-like. This new model is analysed presenting formulations for the reproduction number, sensitivity analysis, and stability analysis for the like-withlike mixing. Insights gained from simulation results on the sensitivity of the model to parameters show the relevance of the activity parameter over the reproduction number when heterogeneous mixing is present.
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