The SIR Model For HIV In Kenya
Introduction
Growing up in Kenya, that has the joint fourth largest HIV epidemic in the world, I had the opportunity to volunteer for an organization called ‘Care for Kenya’ that works in the largest urban slum in Africa. I conversed with women that discussed their challenges living in the slum; HIV was frequently mentioned as a growing issue. I became interested to learn more about the dynamics of how the virus is spread, specifically for Kenya. I came across the SIR model when researching the spread of epidemics, and decided to use it in my exploration to mathematically model the spread of HIV in Kenya. In addition to this, the Euler method for solving differential equations became an interest to me, using it I aim to deepen my understanding …show more content…
This model was developed by Kermak and McKendrick in 1927. In this exploration time will be referred to as (t), and will be the independent variable. The dependent variables are; (S) that represents those susceptible to the infection at time (t), (I) that represents those infected at time (t) and (R) that represents those that are removed at time (t). In the case of HIV, a cure hasn’t been discovered therefore (R) is removed and not …show more content…
The removal rate: Applying the formulas explained previously in the exploration, the fraction of those removed at time t can be determined by the formula 1/k. In the case of Kenya, approximately 800 people die every day.
800/1500000 = 1/1875 or in decimal 0,00053333
The model assumes this rate is constant throughout and is therefore unprecise, as having a constant rate of removal is not likely over a long period of time and depends on several different variables, making the calculations and predictions of the model not completely accurate.
The infection rate: As mentioned earlier there are βStIt people that become infected for every change in t. For this investigation, an estimate will be made for the infection rate. In Kenya, approximately 100,000 people are infected by HIV per year therefore 100,000/ 44,550,302 gives us the value of 0.002245 as the estimate infection rate.
Powersim
The model bellow, using Kenya’s statistics, was created using the simulation program Powersim. The model used time in years on the x-axis, and the number of people along the y-axis. Table 1 in the appendix, gives evidence of the variables for the stages in the model,
Growing up in Kenya, that has the joint fourth largest HIV epidemic in the world, I had the opportunity to volunteer for an organization called ‘Care for Kenya’ that works in the largest urban slum in Africa. I conversed with women that discussed their challenges living in the slum; HIV was frequently mentioned as a growing issue. I became interested to learn more about the dynamics of how the virus is spread, specifically for Kenya. I came across the SIR model when researching the spread of epidemics, and decided to use it in my exploration to mathematically model the spread of HIV in Kenya. In addition to this, the Euler method for solving differential equations became an interest to me, using it I aim to deepen my understanding …show more content…
This model was developed by Kermak and McKendrick in 1927. In this exploration time will be referred to as (t), and will be the independent variable. The dependent variables are; (S) that represents those susceptible to the infection at time (t), (I) that represents those infected at time (t) and (R) that represents those that are removed at time (t). In the case of HIV, a cure hasn’t been discovered therefore (R) is removed and not …show more content…
The removal rate: Applying the formulas explained previously in the exploration, the fraction of those removed at time t can be determined by the formula 1/k. In the case of Kenya, approximately 800 people die every day.
800/1500000 = 1/1875 or in decimal 0,00053333
The model assumes this rate is constant throughout and is therefore unprecise, as having a constant rate of removal is not likely over a long period of time and depends on several different variables, making the calculations and predictions of the model not completely accurate.
The infection rate: As mentioned earlier there are βStIt people that become infected for every change in t. For this investigation, an estimate will be made for the infection rate. In Kenya, approximately 100,000 people are infected by HIV per year therefore 100,000/ 44,550,302 gives us the value of 0.002245 as the estimate infection rate.
Powersim
The model bellow, using Kenya’s statistics, was created using the simulation program Powersim. The model used time in years on the x-axis, and the number of people along the y-axis. Table 1 in the appendix, gives evidence of the variables for the stages in the model,