Stigma toward people living with HIV/AIDS (PLWHA) has impeded the response to the disease across the world. Widespread stigma leads to poor adherence of preventative measures while also causing PLWHA to avoid testing and care, delaying important treatment. Stigma is clearly a hugely complex construct. However, it can be broken down into components which include internalized stigma (how people with the trait feel about themselves) and enacted stigma (how a community reacts to an individual with the trait). Levels of HIV/AIDS-related stigma are particularly high in sub-Saharan Africa, which contributed to a surge in cases in Kenya during the late twentieth century. Since the early twenty-first century, the United Nations and governments around the world have worked to eliminate stigma from society and resulting public health education campaigns have improved the perception of PLWHA over time, but HIV/AIDS remains a significant problem, particularly in Kenya. We take a data-driven approach to create a time-dependent stigma function that captures both the level of internalized and enacted stigma in the population. We embed this within a compartmental model for HIV dynamics. Since 2000, the population in Kenya has been growing almost exponentially and so we rescale our model system to create a coupled system for HIV prevalence and fraction of individuals that are infected that seek treatment. This allows us to estimate model parameters from published data. We use the model to explore a range of scenarios in which either internalized or enacted stigma levels vary from those predicted by the data. This analysis allows us to understand the potential impact of different public health interventions on key HIV metrics such as prevalence and disease-related death and to see how close Kenya will get to achieving UN goals for these HIV and stigma metrics by 2030.

The 2014–2016 West African outbreak of Ebola Virus Disease (EVD) was the largest and most deadly to date. Contact tracing, following up those who may have been infected through contact with an infected individual to prevent secondary spread, plays a vital role in controlling such outbreaks. Our aim in this work was to mechanistically represent the contact tracing process to illustrate potential areas of improvement in managing contact tracing efforts. We also explored the role contact tracing played in eventually ending the outbreak. We present a system of ordinary differential equations to model contact tracing in Sierra Leonne during the outbreak. Using data on cumulative cases and deaths, we estimate most of the parameters in our model. We include the novel features of counting the total number of people being traced and tying this directly to the number of tracers doing this work. Our work highlights the importance of incorporating changing behavior into one’s model as needed when indicated by the data and reported trends. Our results show that a larger contact tracing program would have reduced the death toll of the outbreak. Counting the total number of people being traced and including changes in behavior in our model led to better understanding of disease management.

Crime data provides information on the nature and location of the crime but, in general, does not include information on the number of criminals operating in a region. By contrast, many approaches to crime reduction necessarily involve working with criminals or individuals at risk of engaging in criminal activity and so the dynamics of the criminal population is important. With this in mind, we develop a mechanistic, mathematical model which combines the number of crimes and number of criminals to create a dynamical system. Analysis of the model highlights a threshold for criminal efficiency, below which criminal numbers will settle to an equilibrium level that can be exploited to reduce crime through prevention. This efficiency measure arises from the initiation of new criminals in response to observation of criminal activity; other initiation routes - via opportunism or peer pressure - do not exhibit such thresholds although they do impact on the level of criminal activity observed. We used data from Cape Town, South Africa, to obtain parameter estimates and predicted that the number of criminals in the region is tending towards an equilibrium point but in a heterogeneous manner - a drop in the number of criminals from low crime neighbourhoods is being offset by an increase from high crime neighbourhoods.

The interplay between criminal activity and crime control/prevention measures is inherently dynamic. This paper presents a simple nonlinear dynamical system in which criminal activity levels are coupled to policing effort. Through the process of non-dimensionalisation and sensitivity analysis, policing efficiency and the responsiveness of policing effort are identified as key parameter groupings. An analysis of the system shows that bi-stability is a feature of the dynamics. When there is no feedback between criminal activity and police recruitment, a saddle-node bifurcation occurs and threshold levels of criminal activity are required for the activity to be maintained. When feedback is permitted, we also find a backward bifurcation and criminal activity can be contained for policing efficiency below its threshold level. We demonstrate proof of concept for how the model might be used as a predictive tool with real data.