# Agent behavior

Demographic Behavior
As already stated in the General Model Layout, the behavior of the agents can be differentiated into demographic, social and sexual behavior. As we don’t include migration into the model, the demographic behavior reduces to births and deaths inside the population. From AGE and SEX it is relatively simple to define a function for the DEATH of an agent, taking data from a life-table, where you can find the yearly probability of survival. Those probabilities are transferred to daily death probabilities via

`1 - (1 - P(DEATH))^(1/365)`

Afterwards a random number is drawn between 0 and 1, and if the random number is smaller or equal the death probability, the agent will set its ALIVE variable to 0 and exit the simulation.

One could follow the same approach for the births, but as we already simulate sexual behavior of agents (see below), we might as well try to simulate pregnancy as a results from sexual intercourse. Starting from right after a sexual act, the behavior of the agents is as follows:

The agent will get pregnant, if it is a female agent younger than 50 years, in its fertile period (1/4 of a month), using no or failing contraception, is not already pregnant or infertile and given the chance of 1/3, that unprotected intercourse during the fertile perion leads to pregnancy (Wilcox et al. 1995). Thereby the failure rate of condoms and the pill are taken from the PEARL-index and the rate of infertile persons is taken from the literature.

To determine wether or not a agent is using no contraception, condoms, the pill or both of the latter is determined by a multinomial-choice model using the mlogit R-package. The model contains AGE, AGE^2, SEX, NOB and the relationship-status as well as several interaction terms between those variables. The coefficient values from the regression model are transferred to the C-code for the agent behavior. Each agent calculates its fitted values (i.e. the probability for each of the alternatives) using the coefficients on his memory variables on its birthday or after a change of the relationship status. Afterwards a random number is drawn which determines the kind ofcontraception used by the agent for this year or until the next relationship change.

If an agent got pregnant, the PREG variable will be incremented every day and a new agent is created after 267.5 ± 17.5 days. However, spontaneous and induced abortions have a significant impact on the number of pregnancies resulting in births. From official statistics we see that roughly 660,000 live births are contrasted by roughly 110,000 induced abortions. In addition, dependent on age we 3,8 to 65,8 percent of pregnancies to result in spontaneous abortions. So, during the pregnancy the child might be lost with the according probabilities.

Social Behavior
The social behavior of agents in the SILAS-model focuses only on “romantic” relationships between agents. In the context of STIs, partnerships are extremely relevant as they limit the number of partners for sexual intercourse. Of course, one could argue, that partners are mostly chosen from the general social network of a person and therefore all social networks should be included. Unfortunately, at the current state of SILAS we want/need to contain the complexity of the model and therefore only model partnerships between agents.

If we want to model relationships dynamically, we need to know when relationships start and when they end. However, as the start of a relationship denotes the end of a person’s single-life, methods for survival analysis can be applied to the duration of the single-times as well as relationship-duration. Nevertheless, for the start as well as for the end of a relationship, there are certain features to be respected in the analysis. On the one hand, the intention or desire for a relationship is decided by a single agent alone. But usually the first single-time in a person’s life, i.e. until the beginning of the first relationship, is much longer than other single-times or the times between the following relationships. On the other hand, the end of an relationship affects two persons and therefore the decision to break up needs to be synchronized between the agents. (Although in reality it may be only one of the partners)

To set up decision rules for agents on the length of single-times and the duration of a relationships, three different Weibull-GLMs/GAMs were estimated. The duration until the first relationship was only estimated in dependence of SEX and the duration of subsequent single-times was estimated with respect to SEX, SEXOR, duration of last relationship, age at the end of the last relationship and interaction terms. The duration of relationships was analyzed under considertation of SEX, SEXOR, the age at the beginning of the relationship and interaction terms. So as in the case of contraception choice, agents calculate their Weibull-distribution of single-times and relationship-times and draw a value from this distribution upon the end of the respective other. The day of the change of the relationship-status is then stored in the BCR-variable and on that day the change takes place. How two agents seeking a relationship are finally brought together will be the topic in the Matching of Agents-section.

Sexual Behavior
The last set of behavior rules regulates the sexual activities of the agents and naturally is the most important part for modeling STIs. Unfortunately, the involvment of two independly acting agents in a single sexual intercourse doesn’t make it an easy task. From a theoretical point of view, a sexual activity takes place if two agents with the same, autonomously built intention meet. As most surveys ask about realized sexual contacts, it is hard to calculate the actual intention. Fortunately, Manuel came up with a solution for agents in partnerships under the simple, but strong assumption of symmetric intention. For the sexual contact of singles we avoid a intention-action framework by setting the intention equal to the action. This means we estimate the probability of a single for a sexual contact from the data. If we transfer these estimates to the model, we need to make sure that every single agents ends up having a sexual contact once the intention is deduced from the behavior rule. Under these constraints, the estimation of actual sexual contacts from the survey data is sufficient for establishing sexual behavior rules.

To retrieve the daily probability of a sexual contact, seperate beta-inflated GLMs/GAMs are estimated for singles and couples as well as for each sexual orientation, respectively. SEX, AGE, NOB, PREG and NOP are included in the “single”-model and supplemented by the duration of the relationship in the “relationship”-model as explanatory variables for all four parameters of the beta-inflated distribution. Again, the results are transferred to the C-code and each agent calculates the beta-inflated distribution of its probability of a sexual contact. It samples a value from this distribution and this value is evaluated to a random number between 0 and 1, leading to sexual contact or no sexual contact. Again, how two single agents with the intention of sexual contact are matched is described in the Matching of Agents-section.

 Behavior Distribution Model type Parameters estimated independent variables Time to first relationship Weibull, GLM mu, sigma SEX Time to next relationship Weibull, GAM mu, sigma SEX, SEXOR, duration last relationship, Age at end of last relationship Duration of relationship Weibull, GAM mu, sigma SEX, SEXOR, Age at begin of relationship Probability of sexual contact in relationshipstratified by SEXOR beta-inflated, GAM mu, sigma, nu, tau SEX, AGE, NOB, PREG, NOP, duration of relationship Probability of single sexual contactstratified by SEXOR beta-inflated, GAM mu, sigma, nu, tau SEX, AGE, NOB, PREG, NOP

Table: Overview of GAMs/GLMs to estimate agent behavior.