+

Compartmental Model for Chlamydia, a Sexually

Transmitted Disease

Figueroa-Monsanto, Héctor L.1

Pedrogo-Flores, Leonardo2

Cruz-Aponte, Mayteé3

Department of Chemistry1, Department of Natural Sciences2, and

Department of Mathematics-Physics3

University of Puerto Rico at Cayey

+Biological Disease: Chlamydia

Bacterium: Chlamydia trachomatis

Chlamydia is the most common sexually transmitted

disease (STD) in the world (Siam, 2012)

Transmission:

Direct contact with any infected area of the

Child Birth

Incubation period: 5 - 21 days

Treatment: Antibiotics

www.allposters.com

+Disease Symptoms

Females

Blood flow between periods

Pain: periods, sex, abdomen, and urination

Vagina itch

Males

Pain: testicles and urination

Penis: swelling, pain, burn, itch, and transparent discharge

Urethritis: 55%

Recovered people could be susceptible again.

+First Research Question

What is the behavior of the model on a

bigger scale?

Bigger scale – population dynamic of disease spreading.

How important is Chlamydia in our community?

+Future Research Question

What is the behavior of the disease in a

lower scale?

Lower scale – on a cellular level within the host using

compartments for the progression of the incubation.

Can our model be more precise using equations that

better model the incubation period?

+Purpose

By this we intend to develop a much more

precise model that simulates the disease at

its best and contributes in a better scale to

the scientific community.

Better define the behavior of the chlamydia

disease on a lower scale.

+ Schematic of disease dynamics:

Mathematical Model

S

E

I

R

βSI/N

αE

γI

μR

+ Schematic of disease dynamics:

Parameters

Parameter Description Range/Value References

β Probability of obtaining

the bacteria 67% Potterat (1999)

1/α Incubation Period 5 - 21 days http://www.antimicrobe.org/m04.asp

1/γ Days of Recovery if

treated

7 days with

treatment

http://www.cdc.gov/std/treatment/2010

/chlamydial-infections.htm

1/μ

# days after recovery

that the person waits to

be sexually active again

7 days http://www.cdc.gov/std/treatment/2010

/chlamydial-infections.htm

+Results: Chlamydia Disease Trend

+Mathematical Analysis

Equilibrium points:

−𝛽𝑆𝐼

𝑁+ 𝜇𝑅 = 0 → −

𝛽𝑆

𝑁+ 𝛾 𝐼 = 0

𝛽𝑆𝐼

𝑁− 𝛼𝐸 = 0 →

𝛽𝑆

𝑁− 𝛾 𝐼 = 0

𝛼𝐸 − 𝛾𝐼 = 0 → 𝐸 =𝛾𝐼

𝛼

𝛾𝐼 − 𝜇𝑅 = 0 → 𝑅 =𝛾𝐼

𝜇

Disease Free Equilibrium 𝑁, 0,0,0 "Trivial Solution”

Unstable

Endemic Equilibrium𝛾𝑁

𝛽,𝛾𝐼∗

𝛼, 𝐼∗,

𝛾𝐼∗

𝜇, 𝐼∗ ≠ 0

Stable

+Results

Using the endemic equilibrium point

and the fact that our population is constant:

Infected Individuals at the endemic stage:

Range:

Between 16% – 29%

of the population.

+Endemic Equilibrium Point

Solving for I we established the general equation:

𝐼∗ = 𝑁𝛽 − 𝛾

𝛽

𝛼𝜇

𝜇𝛾 + 𝜇𝛼 + 𝛼𝛾

The specific case of our scenario:

𝐼∗ = 1 −1

.67(7)

17𝑥

149

+ 217𝑥

Varying our incubation period (5,15, 21) days:

𝐼∗ 5 = 1 −1

.67(7)

1

7(5)1

49+2

1

7(5)

= 0.29

𝐼∗ 15 = 1 −1

.67(7)

1

7(15)1

49+2

1

7(15)

= 0.19

𝐼∗ 21 = 1 −1

.67(7)

1

7(21)1

49+2

1

7(21)

= 0.16

+Endemic Equilibrium Point Graph

+Graphical perturbation and

stability of the equilibrium point.

+R0 Basic Reproductive Number

(Using the Next Genertation Operator)

ℱ =𝛽𝑆𝐼

𝑁0

⇒ ℱ =0 𝛽0 0

𝒱 =𝛼𝐸

−𝛼𝐸 + 𝛾𝐼⇒

𝛼 0−𝛼 𝛾

⇒ 𝒱−1 =

1

𝛼0

1

𝛾

1

𝛾

R0=𝜌 ℱ𝒱−1 = 𝜌0 𝛽0 0

1

𝛼0

1

𝛾

1

𝛾

R0= 𝛽

𝛾= 7(.67)= 4.69

+Basic Reproductive Number For

Known Diseases

+Future Work

Develop and agent-base model for a given

population.

Modify schematic model by inserting new

equations that specify on the behavior of

the disease during its period of incubation.

+Bibliography

Al-Mously N, Eley A. 2015. Transient exposure to Chlamydia

trachomatis can induce alteration of sperm function which cannot be

stopped by sperm washing. Middle East Fertility Society Journal 20,

48-53. doi:10.1016/j.mefs.2014.04.003.

Borges V, Gomes JP. 2015. Deep comparative genomics among

Chlamydia trachomatis lymphogranuloma venereum isolates

highlights genes potentially involved in pathoadaptation. Infection,

genetics and Evolution 32, 74-88. doi:10.1016/j.meegid.2015.02.026.

De Borborema-Alfaia APB, de Lima Freitas NS, Filho SA, Borborema-

Santos CM. 2013. Chlamydia trachomatis infection in a simple of

northern Brazilian pregnant women: prevalence and prenatal

importance. Braz J Infect Dis 17(5):545-550.

doi:10.1016/j.bjid.2013.01.014.

Departamento de Salud. 2012. Datos de Puerto Rico.

http://www.estadisticas.gobierno.pr/iepr/LinkClick.aspx?fileticket

=RVOVIk8ka1A%3D&tabid=186.

+Bibliography

Knittler MR, Berndt A, Böcker S, Dutow P, Hänel F, Heuer D,

Kägebein D, Klos A, Koch S, Liebler-Tenorio E, Ostermann C,

Reinhold P, Saluz HP, Schöfl G, Sehnert P, Sachse K. 2014.

Chlamydia psittaci: New insights into genomic diversity, clinical

pathology, host-pathogen interaction and anti-bacterial

immunity. International Journal of Medical Microbiology 304,

877-893. doi:10.1016/j.ijmm.2014.06.010.

Occhionero M, Paniccia L, Pedersen D, Rossi G, Mazzucchini H,

Entrocassi A, Vaulet LG, Gualtieri V, Fermepin MR. 2015.

Prevalencia de la infección por Chlamydia trachomatis y factores

de riesgo de infecciones transmisibles sexualmente en

estudiantes universitarios. Rev Argent Microbiol 47(1): 9-16.

doi:10.1016/j.ram.2014.11.003.

Siam EM, Hefzy EM. 2012. The relationship between antisperm

antibodies prevalence and genital Chlamydia trachomatis infection

in women with unexplained infertility. Middle East fertility Society

Journal (2012) 17, 93-100. doi:10.1016/j.mefs.2011.09.003.

+Acknowledgments

Mentors:

Dr. Mayteé Cruz-Aponte

Danilo Pérez-Rivera

+