Abstract: Evidence suggests a strong correlation between the prevalence of HSV-2 (genital herpes) and the perseverance of the HIV epidemic. HSV-2 is an incurable viral infection, characterized by periodic reactivation. We construct a model of the co-infection dynamics between the two diseases by incorporating a time-since-infection variable to track the alternating periods of infectiousness of HSV-2. The model considers only heterosexual relationships and distinguishes three population groups: males, general population females, and female sex workers. We calculate the basic reproduction numbers for each disease that provide threshold conditions, which determine whether a disease dies out or becomes endemic in the absence of the other disease. We also derive the invasion reproduction numbers that determine whether or not a disease can invade into a population in which the other disease is endemic. The calculations of the invasion reproduction numbers suggest a new aspect in their interpretation – the class from which the initial disease carrier arises is important for understanding the invasion dynamics and biological interpretation of the expressions of the reproduction numbers. Sensitivity analysis is conducted to examine the role of model parameters in influencing the model outcomes. The results are discussed in the last section.

Abstract: Background
In 2002, Chile introduced a major health reform, designed to level out inequities in healthcare coverage, access and opportunities. In particular, the opportunity guarantees ensure a maximum time to receive the appropriate diagnosis and treatment, and thus, gender bias should not be observed.
Objective
To explore the existence of differences in the timeliness of treatment between women and men under the Chilean public health insurance system. We controlled by other observable variables, including age, insurance holder status, provider complexity and health district.
Methods
We used an individual level database that includes all interactions for the diseases covered under the national plan from 2014 to 2019. We excluded from the analysis the diseases affecting only men, women, and infants. To study the waiting time differences between women and men, we first perform a Welch two sample t-test. Then, we used a multilevel hierarchical regression model to further explore the impact of gender in waiting time. At the individual level, we included gender, insurance holder status, age, and the interaction between gender and age. For the aggregate levels, we used the specific opportunity guarantee, the type of provider, and health district.
Results
From the Welch two sample t-test, we found significant differences in waiting times between women and men, in seven opportunity guarantees. From the multilevel regression, the individual variables: holder status, ages between 35 and 49, and the interaction between gender and age for ages between 40 and 54 were statistically significant at 95% level. We remark that the major differences in waiting times between women and men were observed for individuals between ages from 40 to 54, with women waiting significantly longer.
Conclusion
Results show the existence of bias in the timeliness of treatment, proving that universal guarantees are not enough to reduce gender inequalities in health care.