1. Modeling Natural History of Syphilis in Prison Population
Exhibitor: Daniel Ramírez
Teacher: Pablo Aguirre
Professionals UDD: Carla Castillo
Manuel Nájera

2. Summary
Syphilis is a systemic bacterial infection caused by Treponema pallidum.
The most likely cause of transmission of this disease is sexually, and if not treated on time can even cause death.
Syphilis is classified as an STD.

3. What about people in prison?
Periodic overcrowding
Sexual domination
Poor access to health
While maintaining a steady stream of inmates who may
already be infected.

4. Objective:
See the states or steps that it can take from an initial criminal population.
Adjusting variables and parameters necessary to obtain a prevalence of around 3 percent.
Find the critical parameters affecting the morbidity of the disease.

5. Biological model The development model is based
on the diagram 1, which represents
progress in stages of the disease,
including treatment, as this
progresses in a susceptible individual
Diagram 1

6. Background The variables and parameters used in developing the model
with their respective values and units, and adjusted to actual
conditions in penitentiaries, are presented in the following tables:
Table 1

7. Table 2

8. Table 3

9. Mathematical model Taking into consideration the biological model,
together with the variables and parameters shown,
we have the following model:

10. Results Variation of susceptible people Graph 1 Syphilis initial model
Variation only τ1 and τ2
Final model with parameters
adjusted to jail
Graph 1

11. Where i0 is the starting point, and if the end point:
Table 4
It is seen that the prevalence of infection in the prison is 2.84%.

12. Conclusions It is highly dependent on the model to small
Number of susceptible as it changes τ1
It is highly dependent
on the model to small
variations in the
parameters τ1 and τ2
Graph 2

13. An increase in rate of treatment, involves an increase in the number
Number of susceptible as it changes τ2
An increase in rate of treatment,
involves an increase in the number
of susceptible
Graph 3

14. Using new methods of
detection of syphilis which
directly influence the rising
rates of treatment in prison,
carries a lower prevalence
of this disease, and therefore
more effective in the detection
of syphilis.

15. Extensions Input screening with quick test.
Test new methods in this model as an:
Input screening with quick test.
Sreening massive with quick test.
Use quick test before consultation.
Then determine the cost effectiveness of each method and
construct a decision model.

16. Thank you for your attention.