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.

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.

In this paper, the global properties of a classical Kaposi's sarcoma model are investigated. Lyapunov functions are constructed to establish the global asymptotic stability of the virus free and virus (or infection) present steady states. The model considers the interaction of B and progenitor cells in the presence of HHV-8 virus. And how this interaction ultimately culminates in the development of this cancer. We have proved that if the basic reproduction number, 0  is less than unity, the virus free equilibrium point, ε 0 , is globally asymptotically stable (GAS). We further show that if 0  is greater than unity, then both the immune absent and infection persistent steady states are GAS.

Kaposi’s sarcoma (KS) is a malignant disorder of lymphatic endothelial origin that can have two main variants: AIDS-related KS (AKS) and non-AIDS related KS (NAKS) that all share a causal relationship with the human herpesvirus-8 (KSHV or HHV-8). We develop a mathematical model that accounts for B-cells latently and lytically infected with HHV-8 as well as the innate and adaptive arms of the immune system. As a sequel to numerous studies that have investigated the inhibition of HHV-8 endocytosis and reactivation of HHV-8 replication, we employ optimal control strategy to obtain treatment efficacies for these two therapeutic approaches. We have shown that when [Formula: see text] of the B-cell infections result in latency, administration of high efficacy drugs that inhibit entry and reactivation of latently infected B-cells leads to the clearance of KS as the population of infected cells cannot be sustained. Our results also reveal that at [Formula: see text] latency of B-cells, the therapy could produce similar results if the drug that targets viral entry is of moderate efficacy but the efficacy of the drug inhibiting reactivation is considerably more than [Formula: see text] Administration of the same drugs but both at moderate efficacy levels leads to the depletion of both uninfected B- and progenitor cells, a scenario which can lead to the growth of KS variants. When [Formula: see text] of the B-cell infections result in latency, administration with high efficacy drugs reduces the viral entry of HHV-8 but as [Formula: see text] of the infected B-cells are productive, this event leads to production of HHV-8 which ultimately results in more progenitor cells getting infected and the growth of KS. Our findings have the potential to offer more effective therapeutic approaches in the treatment of NAKS.