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.
<abstract><p>As potential strategies to control the spread of COVID-19, governments all across the globe have implemented interventions such as lockdowns and confinement. While these strategies have helped to control the spread, there have also been evidence of widespread increase in Domestic Violence (DV) which is often under-reported. In this work, we have developed two new models that will help study the relationship between lockdowns, the spread of COVID-19 and DV in the hope of mitigating the social problems that follow such drastic measures. Two different models, in increasing level of complexity have been employed to simulate the effect of the lockdown strategy in the spread of COVID-19 and DV. One of the models simulates the spread of DV under three different lockdown scenarios: one long period, two and three shorter intervals that comprise the same interval of time since onset of the Pandemic. Another model studies the interaction between COVID-19 and DV during confinement in relation to the length of the lockdowns. Our findings indicate multiple lockdowns are safer for DV but not necessarily for controlling spread of COVID-19. We also present a derivation of the basic reproduction number for the model involving the interaction between COVID-19 and DV.</p></abstract>
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