Simulation of spreading of sexually transmitted infections

Introduction

Spreading of sexually transmitted infections such as HIV is not yet fully understand phonenomena. The problem with statistics is that he real number of HIV possitive people is latent. Only the number of people which know about their infections is known. The real number of people which are infected must be only estimated. One of methods of how this number can be estimated is by agent based simulation where agents - people behave similarily to real people.

Software

NetLogo 6.0 (Decemeber 20, 2016)

Methods, limitations and goal

The speed of speding of sexually transmitted infections depends mainly on sexual behavoir of people. The behavior of agents was set to follow the answers from behavioral researches. The goal is that the simulation will be approximation of reality. Since it is hard to simulate whole world the simulation is limited to one relatively closed place. The people in simulation cannot move to other locality and other people do immigrate to the simulation. We conjecture that migration to and from nearby towns and cities would not have big impact since it is almost equivalent to dying agents and to new agents being born from the observers view.

However background reaseach showed that other factors impact the number of HIV positive people which is not not captured by the simulation. The main of them is tourism. It is evident that the infection speads in tourstical destinations and by the flow of turists. Even in czech republic the increase of new HIV possitive people corellates with the popularity of turistical destinations such as Thailand.

We omit this, other political and demographical problems and simulate only the simplest sexual behaviour of people. People in this simulation can be born eaither healthy or infected depending on whether the mother is infected or not. Everybody is either heterosexual, homosexual or bisexual. People start looking for similar partner at the age of pubescence and might change partner several times during life. (Honest veterans can exist, but it is rare.) Pairs then have sex iregularily several times per month. Every pair in the simulation uses bairer protection such as condoms in the beggining of partnership and later stops using it if the partnership lasts for some random time. At the times when the pair doesn't use such protection the infection can be transmited with certain.

Some people also take drugs introvenously in the simulation which can cause them being infected too.

Behavioral parameters which were set to be the same as in reality

Age when person starts sexual life

Length of year - 365.25

Lifeexpectancy - 78 years

Probability of using a drug - 0.05

Average number of children per mother - 2.00

Average number of partners per life - 10

Probability of bisexual behavior 18%

Probability of beeing homosexual 4%

The frequency of sex once per 8 days in hererosexual pairs. More often in gay pairs and less often in lesbian pairs

Average time which people spend by searching for partner 1.5 years.

Probability of giving girth to boy or girl, 50% boy, 50% girl

The numbers are often not exact in cited sources. They are specified as intervals or they even differ between different sources. So the numbers come from cited sources but I rounded them myself and I often choose some middle value myself.

Especially problematic is the number of partners. According to background research the number of partners of average girl and of average boy. Girls were supposed to change 8 boys during life. But boys were supposed to change 12 girls during life. It is impossible since the number of boys and girls is similar. The difference is probably caused by the people lying in researches. That is why I set the number to 10.

Infection transmission probabilities

These parameters are also not known exactly and they differ between different infection HIV/sifilis/other. The default values in simulation are set to fit HIV.

The serios literature doesn't specify the probabilites exactly but only as interval estimate. The probability of mother to child transmission is supposedly 10 - 20%.

The real probability of transmission of desease by sexual intercourse is much more complicated and depends on many factors. It depends on the length and intenzity of intercourse and on degree of injury to the mucosa. After a consultation with a friend from K-Centrum Liberec I set this probability to 0.08.

Both parameters can be set by user using a slider. This way use can run simulation and see what happens when he or she has diferent knowleadge or if he wants to see results for different desease.

Parameters which are not the same as in reality

Even though it was possible to find estimates of real-valued parameters their distribution often doesn't follow reality exactly in this simulation. I often used the found values to generate distribution with the same expected value and sometimes with the same standard deviation but not exactly from the same distribution.

The lenght of life is generated from truncatenated normal distribution. Womens give births to children with specified probability given by formula which says that expected number of children a women with average length of life is 2.0. So only the average number of childrens fits the realtity. Not the probability distribution of this number.

Simiarly other vere generated the way that their expected value should fit the reality. But their distribution is collary of used algorithm. Namely: The number of partners follows approximately poisson distribution, the time to find partner follows approximately geometric distribution. The time a person insists on using a condom is drawn from uniform distribution between 0 and 1 year at the time a person is born. Since in the simulation both partners are required to agree with not using the condom the collary is that the time a pair uses a condom is from triangular probability distribution, the time spent with a partner follows geometric distribution.

Simulation details

Properties of a person in simulation

Most of the properties of a person is determined at the moment when a person is born.

These properties include:

• Length of life
• Sexual appetatite
  • Mans has this quantity higher than womans.
  • These values from both partners are used to compute the probability that partners will have sexual intercourse (see algorithm bellow) and its expected frequnecy fits the real values.
• gender
• sexual orientation
• age when person starts sexual life
• drug taking probability
• frequency of sharing a needle
• degree of bisexuality

Basics

The world is simulated day by day. Each day each agent is asked to live its one day. Each day the agent checks if its age is less then the spefied date of death and possibly dies. Each day each engaged agent consides whether to change partner. With probability p it breaks with partner and tries to find someone else with probability (1-p) it stays with the same partner. That is why the time spent with one partner follows geometrical distribution. p is computed by a formula so the expected time spent with a partner fits the reality.

Each day every person decides whether it wants to date that day. This decision is from alternative distribution with p as above for engaded people and smaller p for single people, where p for single people is set to the way that average time spent without partner fits the reality.

Afterwards all people which want to date that day (both signgle and engaded) are processed by partner searching alorithm. Afterwards