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MBE, 20 (9): 16131–16147.
DOI: 10.3934/mbe.2023720
Received: 01 June 2023
Revised: 17 July 2023
Accepted: 30 July 2023
Published: 09 August 2023
http://www.aimspress.com/journal/MBE
Research article
The effect of screening on the health burden of chlamydia: An evaluation
of compartmental models based on person-days of infection
Jack Farrell, Owen Spolyar and Scott Greenhalgh*
Department of Mathematics, Siena College, Loudonville, NY, USA
* Correspondence: Email: sgreenhalgh@siena.edu.
Abstract: Sexually transmitted diseases (STDs) are detrimental to the health and economic well-being
of society. Consequently, predicting outbreaks and identifying effective disease interventions through
epidemiological tools, such as compartmental models, is of the utmost importance. Unfortunately, the
ordinary differential equation compartmental models attributed to the work of Kermack and
McKendrick require a duration of infection that follows the exponential or Erlang distribution, despite
the biological invalidity of such assumptions. As these assumptions negatively impact the quality of
predictions, alternative approaches are required that capture how the variability in the duration of
infection affects the trajectory of disease and the evaluation of disease interventions. So, we apply a
new family of ordinary differential equation compartmental models based on the quantity person-days
of infection to predict the trajectory of disease. Importantly, this new family of models features non-
exponential and non-Erlang duration of infection distributions without requiring more complex
integral and integrodifferential equation compartmental model formulations. As proof of concept, we
calibrate our model to recent trends of chlamydia incidence in the U.S. and utilize a novel duration of
infection distribution that features periodic hazard rates. We then evaluate how increasing STD
screening rates alter predictions of incidence and disability adjusted life-years over a five-year horizon.
Our findings illustrate that our family of compartmental models provides a better fit to chlamydia
incidence trends than traditional compartmental models, based on Akaike information criterion. They
also show new asymptomatic and symptomatic infections of chlamydia peak over drastically different
time frames and that increasing the annual STD screening rates from 35% to 40%-70% would annually
avert 6.1-40.3 incidence while saving 1.68-11.14 disability adjusted life-years per 1000 people. This
suggests increasing the STD screening rate in the U.S. would greatly aid in ongoing public health
efforts to curtail the rising trends in preventable STDs.
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Keywords: Chlamydia trachomatis; mean residual waiting-time; hazard rate; disability adjusted life-
years; differential equations; compartmental model
Abbreviations: ODE – Ordinary Differential Equation; STD – Sexually transmitted disease; STI –
Sexually transmitted infection; PID – Pelvic inflammatory disease; HIV – Human immunodeficiency
virus; DALY – Disability adjusted life-years; AIC – Akaike information criterion; RSS – Residual
Sum of Squares
1. Introduction
Sexually transmitted infections (STIs) have seen sharp climbs in incidence, with a ~30% increase
in the U.S. [1] between 2015 and 2019. This trend will likely be further exacerbated due to the COVID-
19 pandemic as evidence mounts on the social effects of lockdowns, the reduction in STI testing over
the pandemic [2] and the diversion of health resources to more pressing matters [3]. While all STIs are
of concern, chlamydia, in particular, represents a substantial health risk for the U.S. since it is the most
common STI, at a staggering 1.8 million incidences [4]. In part, the reason for the high incidence is
the ease with which it spreads, as transmission commonly occurs through vaginal, anal or oral
intercourse and possible mother-to-child transmission during childbirth [5]. Chlamydia is also
associated with myriad negative health outcomes including infertility [6], lymphogranuloma venereum [7],
conjunctivitis [8], an increased risk of acquiring HIV [9] and social stigma [10], among numerous
others. Consequently, action is required to stop the rising incidence of chlamydia, particularly through
the effective deployment of health interventions.
To mitigate the spread of chlamydia, health authorities recommend several health policies. The
simplest is recommending abstinence from sexual intercourse to younger demographics [5], in addition
to practicing safe sex for all sexually active individuals. Health authorities also recommend that at-risk
groups, namely women, gay and bisexual men younger than 25 years [5], annually screen for
chlamydia, especially for those with multiple sexual partners [5]. To communicate these
recommendations, awareness campaigns on STIs are periodically launched targeting these
demographics to illustrate the impact of STIs on life, reduce STI-related stigma and ensure people
acquire the tools and knowledge to prevent and test for infection [11]. Fortunately, even if these health
interventions fail and chlamydia infection occurs, effective antibiotics treatments are available, such
as the use of azithromycin [12] or doxycycline [13,14]. Unfortunately, due to the delays in the
appearance of symptoms and seeking of treatment, an infection can negatively affect reproductive
health in both men and women. Pregnant women in particular face severe risk since chlamydia
infection may cause a fatal ectopic pregnancy or even permanent damage to their reproductive systems
through pelvic inflammatory disease (PID) [5].
The recent uptick of chlamydia incidence in the U.S. calls to light an urgent need to evaluate
strategies that may curtail the trend. To inform on such strategies, we evaluate the role that screening
may have in reducing chlamydia incidence and the effects of symptomatic and asymptomatic durations
of infection. To account for the variation in symptomatic and asymptomatic durations of infection on
the trajectory of disease, we develop a mathematical model that permits non-exponential and non-
Erlang distributed durations of infection. Typically, such a feature requires model formulations as
systems of integral or integrodifferential equations [15,16] which are often regarded as beyond the
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capabilities of modelers in public health without specialist training [17]. Herein is part of the novelty
of the presented work, as we further develop a mathematical framework that permits non-exponential
and non-Erlang distributed durations of infection while retaining model formulation as a system of
ODEs. While such a framework has been developed under the context of SIS and SIR models [18,19],
it has yet to be cast into more elaborate compartmental models such as a SEAIR analog [20].
To illustrate the utility of a generalized SEAIR model (gSEAIR) that describes the time evolution
of person-days of infection of chlamydia, we apply it to evaluate the effects of STD screening
interventions on the sexually active population in the U.S. Unlike prior works on generalized
differential equation compartmental models, we consider a model that describes the trajectory of
person-days of infection based on two durations of infection, namely the durations of asymptomatic
and symptomatic chlamydia infection. We use the gSEAIR model to measure how changes in the shape
of the duration of infection distributions affect the quality of fit to data based on Akaike information
criterion (AIC) and subsequently measure how increases in STD screening alter predictions on
incidence averted and disability adjusted life-years (DALYs) saved over a five-year horizon.
2. Materials and methods
In what follows, we detail our mathematical model of chlamydia transmission, as characterized
by a system of ordinary differential equations (ODEs). The model describes the evolution of the
quantity of person-days of infection [18,19], which is based on the multiplication of incidence and a
time-varying average duration of infection. So, we also provide details on the formulation of the time-
varying average durations of infection, i.e., the mean residual waiting-times of infection, in addition
to model parameters, goodness of model fit to data, the calculation of incidence averted and DALYs
averted for each intervention scenario.
2.1. Mathematical model
We developed a compartmental model to predict the spread of chlamydia infection across the
population of the U.S. The model considers five main compartments. Each compartment has two
components: number of people and duration. Thus, we have the person-days susceptible to infection
(), person-days latently infected (), person-days asymptomatically infectious (), person-
days symptomatically infectious () and person-days removed from infection (), where is the
average duration of chlamydia infection, is the mean residual waiting-time of symptomatic
chlamydia infection at time and is the mean residual waiting-time of asymptomatic chlamydia
infection at time . The rates of transition between each compartment are given by
()
= (+)
+ + + ,
()
= (+)
,
()
= (+ 1)
,
(
)
= (1) (
+ 1)
,
(1)
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()
= (+ 1)
+ (+ 1)
.
Here, denotes the time derivative of , is the per capita birth rate, is the transmission rate,
is the sexually active population of the U.S., 1/ is the incubation period of chlamydia infection and
1/ represents the average duration of immunity to chlamydia infection. Additionally, the time-
varying average duration of infection is calculated by
=(1)+,
where is the proportion of asymptomatic incidence.
For our model, we consider different functional forms of mean residual waiting-times. First, we
assume the classical scenario when the duration of infection is exponentially distributed, which results
in a constant mean residual waiting-time. Specifically, when , and are constants, system (1)
reduces to the classical SEAIR model. Next, we consider a generalization of a family of distributions
with periodic hazard rates [21] that permits multiple troughs and peaks in the average durations of
infection (Supplementary Materials).
Figure 1. Compartmental diagram. The flow of susceptible person-days (), to latently
infected ( ) and either asymptomatically infectious person-days ( ) or
symptomatically infectious person-days ( ) and recovered person days ().
Compartments are composed of individuals multiplied by the time-varying average
duration of infection (), the time-varying duration of asymptomatic infection () or the
time-varying duration of symptomatic infection (). For ease of presentation, birth and
mortality rates are not included (see System 1 for details).
2.2. Parameter estimation and the durations of infection
For our model, we estimate parameters through the literature (Table 1) and published data on
chlamydia incidence [22]. We estimate the average duration of asymptomatic infection with chlamydia
using a synthesis of data on the duration of asymptomatic chlamydia infection [23,24] (Table 1).
Additional model parameters are estimated using a nonlinear least squares procedure, in conjunction
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with Matlab’s ode45 and fmincon algorithms, which fit the SEAIR and gSEAIR models to weekly
chlamydia incidence (Figure 2). Additional parameter details, including those for the calculation of
DALYs, are available in Table 1 and the Supplementary Materials.
Table 1. Parameters, values and sources.
Symbol
Parameter
Base value
Source
Sexually active population
15.5 million
Fit from data
Birth rate/death rate
0.024/year
[25]
Transmission rate
0.050 0.062/year
Table S.1.
1/
Avg. duration of immunity
90 days
[26]
1/
Incubation period
14 days
[26]
Proportion of new infections that are asymptomatic
0.77
[27]
Avg. duration of asymptomatic infection
190 days
[23]
Avg. duration of symptomatic infection
10 days
[28]
Proportion of symptomatic incidence with no complications
0.23
[27]
Proportion of asymptomatic incidence with no complications
0.60
[27]
Proportion of incidence leading to PID
0.09
[28]
Proportion of incidence with epididymo-orchitis
0.0415
[29]
Proportion of PID cases classified as severe
0.175
Supplementary Materials
Proportion of PID cases resulting in death
2.9 ×10
[30]
Avg. duration of uncomplicated symptomatic infection
0.027 years
[28]
Avg. duration of uncomplicated asymptomatic infection
0.521 years
[23]
Avg. duration of moderate PID due to infection
21.01 years
Supplementary Materials
Avg. duration of severe PID due to infection
21.01 years
Supplementary Materials
Average duration of epididymo
-
orchitis and its complications
due to infection
25.38
years Supplementary Materials
Avg. duration of life lost from death due to PID
36.5 years
Supplementary Materials
Avg. time period of reproductive capability in women
39 years
Supplementary Materials
Avg. time period of optimal reproductive capability in men
41.6 years
Supplementary Materials
Avg. time period females are able to reproduce before
contracting chlamydia infection
8.5
years Supplementary Materials
Avg. time period males are able to reproduce before
contracting chlamydia infection
8.6
years Supplementary Materials
Years lost in reproductive capability in women due to PID
9.49 years
Supplementary Materials
Years lost in optimal reproductive capability in men due to
epididymo-orchitis
7.62
years Supplementary Materials
Proportion of chlamydia infections held by women
0.6624
[31]
Disability weight of symptomatic chlamydia with no
complications
0.006
[30]
Disability weight of asymptomatic chlamydia with no
complications
0.0
[30]
Disability weight of incidence leading to PID
0.114
[30]
Disability weight of incidence with epididymo-orchitis
0.128
[30]
Disability weight of PID cases classified as severe
0.324
[30]
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a) b)
Figure 2. Trajectories of new chlamydia incidence and cumulative square error. a) The
trajectory of chlamydia infection in the United States over 175 weeks and b) the square
error of model predictions relative to reported data. Reported incidence (black curve), a
classical SEAIR model fit (= 0, grey curve) and the gSEAIR models with hazard rates
that feature one to nine cosine terms (= 1 to = 9).
To provide insight into the formulation of the duration of infection distribution (,), where
is either for symptomatic infection or for asymptomatic infection, we begin by expressing it in
terms of the recovery rate [32]. Taking (,+) to be the probability of recovery over the time
interval =[,+], we have that (,+)=()
where () is a time-varying recovery rate or equivalently a hazard rate. It follows for small that
we can estimate (+,) as
(+,)(,)1(,+).
Rearranging terms and taking the limit as 0, we have that
(,)=()(,),(,)= 1
or equivalently
(,)=exp ()
.
Traditionally, (,) is exponentially distributed, which is a result of assuming the infectious
period is exponentially distributed [18]. Under such assumptions the hazard rate ()= 1/. Given
this form of hazard rate, the survival function of the duration of infection is
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(,)=exp 1/()
and the mean residual waiting-time is
() =
(,)(,)
=.
Note that because () is constant in this scenario it follows that system (1) reduces exactly to the
traditional SEAIR model.
To evaluate the potential periodicity of the trajectory of chlamydia, we assume a more complicated
form of (,) on both the asymptomatic and symptomatic durations of infection. We consider a
generalization of the simplest probability density function, (), with a periodic hazard rate [21], namely
()=(1cos()),
where is a normalizing constant, > 0, (1,1) and [0,2], to that of a Fourier cosine series,
()=1cos()
,
where > 0, (1,1), ||
< 1 and [0,2].
From the probability density function () and its associated cumulative distribution function, we
obtain the hazard rate (Supplementary Materials)
()=1 cos
1cossin
+
,
with > 0, (1,1), and < 1
. Here, represents the average duration of infection in
the absence of periodic effects and is the amplitude of variation in recovery with frequency 2/,
where the subscript is used to denote either asymptomatic (A) infection or symptomatic (S) infection [33].
Given the hazard rate and its defined relation to the mean residual waiting-time, namely =
(+ 1)/ [33] with (0) = , we have that
()=
1
cos2sin
+
cossin
+
.
2.3. Intervention scenarios and health metrics
To inform on the benefit of awareness campaigns for mitigating chlamydia transmission, we
consider the effects of increasing STI screening rates. We assume that the proportion of people that
get screened within one year [26] follows the distribution
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()= 1 .
Thus, the average time a person has between screenings is
years, which yields the screening rate [26]
=7
365 per week.
Imposing a baseline annual screening rate of 35% [34] of the population, it follows that =
0.0083 per week . Alternatively, if we consider intervention scenarios that increase the annual
proportion of the population screened to 40%, 50% and 70%, we have that = 0.0098 per week,
= 0.0133 per week and = 0.0231 per week respectively.
For these screening rate scenarios, we evaluate our model over 5 years. We estimate incidence
under each mean residual waiting-time by subtracting predictions from 40%, 50% and 70% screening
rates from the baseline. The same approach was also taken to estimate annual DALYs saved, which
were discounted at the standard rate of 5% per year (see Supplementary Materials for further details).
2.4. Goodness of fit
To evaluate the quality of model fit to incidence data, we calculate the AIC [35]. For ease of
presentation, we define the list of variables as : = (,,,,,,) and the list of parameters as
: = (,,,,,,)
when the duration of infection is exponentially distributed and
: = (,,,,,,,...,,,...,,,,...,,,...,)
when the duration of infection follows the distribution with a periodic hazard rate. Thus, defining =
(0,0,0,0,0,(0), (0)), we can represent the ODE system as
: = (,(;); ).
The new symptomatic infections are defined by
(,(;); ) = (1 ).
For these models the residual sum of squares (RSS) is
=((,(;); ))
where is the observed incidence on the week [14,36] and =175 is the number of data points.
Optimal parameters sets,
, and initial conditions
for the distribution types were then
determined by minimizing RSS (Figure 4) through a combination of Matlab’s ode45 and fmincon
algorithms. Thus, given the optimal parameters, it follows that
= ln
+ 2,
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where represents the number of model parameters to be estimated from observed data. The model
with minimum is deemed the best fit.
From the AIC, we approximate the probability that the model is the best candidate among all
models (in the sense of combining accurate predictions while limiting the possible number of
parameters [37]) by calculating AIC weights. First defining =min(), the Akaike
weights [38] for each scenario are
=
.
3. Results
We assessed the effectiveness of the gSEAIR model by estimating the health burden of chlamydia
in the US and informing on the potential health benefits of increasing STI screening rates from the
current annual coverage of 35% to 40%, 50% and 70%, respectively. For these scenarios, we estimated
the annual incidence averted and DALYs averted per year relative to the baseline for both the
traditional SEAIR and gSEAIR models. The gSEAIR models considered feature mean residual
waiting-times for the duration of asymptomatic and symptomatic infection with up to 9 cosine terms
(= 1 to = 9). To identify the most appropriate SEAIR and gSEAIR models, we used AIC in
addition to AIC weights to identify the optimal model and estimate the probability it was optimal
among all considered scenarios.
Our results show that increasing the number of cosine terms in gSEAIR decreases the square error
of model predictions relative to the data (Figure 3). Additionally, the gSEAIR model based on a hazard
rate with six cosine terms is optimal compared to the other candidate models (Figure 3) since it had
the lowest AIC score (Table 2). Conversely, the SEAIR model (i.e., the gSEAIR model with = 0)
had the highest AIC score, with a ΔAIC of 300.6 (Table 2), which indicates it is the least effective of
the modeling scenarios considered. This result is supported by the AIC weights, which indicate that
the = 6 scenario of the gSEAIR model is optimal with a probability of 0.54 (Table 2), where most
other scenarios had ΔAIC scores of at least 4.5 and AIC weights below 0.05. The exception to this is
= 7, where the ΔAIC was 0.81 and the AIC weight was 0.36 (Table 2), suggesting this scenario is
a viable alternative to the = 6.
At a baseline screening rate of 35%, the SEAIR and gSEAIR models predicted 55.5–56.1 annual
incidences of chlamydia per 1000 people. Increasing the screening rate to 40%, 50% or 70% averted
6.1–8.3, 17.5–22.3 and 35.2–40.3 annual incidences per 1000 people respectively, depending on the
number of cosine terms included in the mean residual waiting-times (Table 2). Of these findings, the
gSEAIR model generally predicted a greater benefit when increasing the screening rate to 40%–70%,
with an additional 1.8–4.2 annual incidence averted per 1000 people when compared to the gSEAIR
model (= 6) to the SEAIR model.
Regarding the health burden of chlamydia, we predict increasing the screening rate to screening
rate 40%, 50% or 70% will annually avert 1.68–2.29, 4.83–6.19 and 9.74–11.14 DALYs per 1000
people (Table 3), respectively. Typically, the gSEAIR models predicted a greater quantity of DALYs
averted relative to the SEAIR model, except for the = 1 case (Table 2). When comparing the optimal
gSEAIR model (= 6) to the SEAIR model, predictions illustrate an additional annual 0.51 DALYs
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averted per 1000 people (Table 2). Averaging across all scenarios, annual DALYs averted per 1000
people were 2.06, 5.7 and 10.6 for screening rates of 40%, 50% and 70%, respectively (Table 2).
Figure 3. Akaike information criterion score and square error. The AIC score (solid blue
curve, left axis) and square error (dotted orange curve, right axes) for SEAIR (= 0) and
gSEAIR (= 1 to = 9) models relative to incidence data.
Table 2. Chlamydia incidence averted and DALYS saved for screening rates that achieve 35%, 40%,
50% and 70% coverage of the population per year.
0
1
2
3
4
5
6
7
8
9
AIC Score (1000s)
3.333
3.319
3.318
3.157
3.131
3.124
3.033
3.034
3.037
3.03
AIC Score
300.6
285.7
154.6
123.9
98.0
91.0
0
0.8
4.6
4.8
AIC weights
0
0
0
0
0
0
0.54
0.36
0.05
0.05
Annual incidence/1000 ppl
Baseline ()
55.5
55.9
56.0
55.9
55.6
55.9
55.9
55.9
55.9
56.1
Annual incidence averted (1000 ppl)
40% screened ()
6.3
6.1
7.2
6.8
7.9
7.9
8.1
8.2
8.3
8.2
50% screened ()
17.9
17.5
19.8
19.1
21.8
21.5
22.1
22.3
22.5
22.4
70% screened ()
35.8
35.2
37.6
36.8
39.4
39.3
39.8
40.1
40.2
40.3
DALYs saved per year (1000 ppl)
40% screened ()
1.73
1.68
1.97
1.89
2.17
2.18
2.24
2.24
2.29
2.24
50% screened ()
4.94
4.83
5.46
5.28
6.01
5.93
6.07
6.15
6.19
6.18
70% screened ()
9.89
9.74
10.40
10.18
10.90
10.86
11.01
11.09
11.10
11.14
Averaging all gSEAIR modeling scenarios illustrates the duration of asymptomatic infection
peaked at 32.2 weeks around the 85th week of the outbreak. The symptomatic infection peaked much
earlier, specifically around week 22, with an average duration of 1.9 weeks (Figure 4). Interestingly,
the only mean residual waiting-time (with > 0) that was strictly greater than the constant average
duration of asymptomatic infection for the SEAIR model was the gSEAIR with = 1. In contrast,
mean residual waiting-times were typically less than the average duration of symptomatic infection for
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the SEAIR model, although several cases briefly surpass this value near the end of the outbreak (Figure
4). Towards this regard, when = 5, the mean residual waiting-time for symptomatic infection was
at a minimum (Figure 4), although this may be a result of the associated probability density function
decay rate (Figure 5). For asymptomatic infection, there is not a clear scenario where one of the mean
residual waiting-times is consistently the minimum, as the majority of scenarios appear to converge to
common functions (Figure 4, Figure 5).
a) b)
Figure 4. Mean residual waiting-times of the duration of infection of chlamydia. The
average duration of infection over 175 weeks given a) symptomatic infection and b)
asymptomatic infection. The value of corresponds to the number of cosine terms in the
Fourier cosine series in the probability density function, with = 0 corresponding to an
exponential density function.
a) b)
Figure 5. Probability density functions. The log of probability density functions for hazard
rates with = 0 to = 9 cosine terms for a) the duration of symptomatic infection and
b) the duration of asymptomatic infection.
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For the optimal gSEAIR model (= 6) the cosine terms of the mean residual waiting-times that
are most influential correspond to a period of 82.4 days with an amplitude of 0.22 for symptomatic
infection and 817 days with an amplitude of 0.45 for asymptomatic infection (Table 3). For
symptomatic infection, there were other cosine terms nearly as influential, specifically all amplitudes
from to where close to 0.2. For asymptomatic infection, the term was dominant, with
amplitudes , and all about one-third of its value (Table 3).
Table 3. Duration of infection distribution parameters with periodic hazard rate (= 6).
Symptomatic parameters
Asymptomatic parameters
Amplitude
Period (days)
Amplitude
Period (days)
0.19
2/
198.7
0.45
2/
817.0
0.22
2/
82.4
0.18
2/
97.0
0.19
2/
57.3
-0.04
2/
56.1
0.21
2/
44.0
0.15
2/
45.0
0.02
2/
36.4
0.01
2/
36.5
0.10
2/
30.2
0.17
2/
30.5
4. Discussion
The analysis of our gSEAIR model illustrates it is an effective approach for evaluating the health
burden of chlamydia in the U.S. and in assessing the potential benefits of increasing STI screening
rates. The optimal gSEAIR model, according to measures such as AIC and AIC weights, was the =
6 scenario. This scenario predicted a greater reduction in chlamydia incidence and DALYs when
increasing the annual screening rate from 35% to 40%, 50% or 70%, at least in comparison to the
traditional SEAIR model. Also, our gSEAIR models illustrated that the inclusion of time-varying
average durations of infection (i.e., the mean residual waiting-times) into model dynamics typically
correlated to a greater predicted health benefit from these interventions, at least in comparison to the
classical SEAIR model.
As expected, the scale-up of STI screening causes a reduction in incidence and DALYs. Our
findings illustrate that this reduction is comparable with other STI interventions [39], with the free
distribution of condoms and diaphragms serving as a notable example [40,41]. Our predictions on this
reduction are most likely conservative, as we only account for the effects of STI screening and do not
account for complementary interventions that would be deployed by health authorities including
contact tracing, partner notification [42] and the administration of suppressive therapy [43].
A particular area where the work presented here could be informative is in the rollout of periodic
presumptive treatment [44,45]. To elaborate, the basis of periodic presumptive treatment is the
systematic treatment of at-risk groups periodically with a combination of drugs targeting prevalent
(and curable) STIs, the results of which can cause reductions in STI prevalence up to 50% [45]. Thus,
since our gSEAIR model provides details on multiple periods associated with transmission (i.e., the
periods of the cosine terms in the mean residual waiting-times), it could help to inform on how frequent
periodic presumptive treatment should be deployed to maximize the health benefit of the intervention.
In addition to its potential for informing on public health issues such as periodic presumptive
treatment, our work also opens avenues of mathematical investigation. For instance, most traditional
compartmental models are autonomous systems of nonlinear differential equations whose solutions
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feature a rich history of investigation through Jacobian, next-generation or Routh Hurwitz stability
analysis techniques [46–48], the application of evolutionary invasion analysis to infer the direction of
evolution [25,49,50] or the utilization of optimal control theory to inform on the ideal construction of
public health policies and interventions [51]. In contrast, our model is potentially nonautonomous,
which necessitates the use of Floquet theory [52] or Poincare maps [19] to understand its stability
properties and implications for evolution, which are utilized far less in the realm of mathematical
epidemiology.
Another realm for mathematical investigation is the conversion or comparison of gSEAIR to the
framework of stochastic dynamics [50,53]. For instance, an advantage of many Markov chain models
is the estimation of major and minor outbreak probabilities and their associated durations [54]. Thus,
in theory, a stochastic analog of gSEAIR could inform on the role that the duration of infection
distribution plays in shaping these outcomes. Stochastic differential equations also represent a
potentially fruitful area for future work, as it may be possible to recast their more robust ability to
inform on the evolutionary dynamics of pathogens [55] into a generalized differential equation
compartmental model similar to the ones presented in this work.
Although our model focuses on chlamydia transmission in the U.S., it could easily be adapted to
study other STD outbreaks such as syphilis [56], gonorrhea [19,57], hepatitis [46] and even HIV and
malaria co-infection [58] in other population demographics. Further potential generalizations and
refinements include the addition of disease states such as super-spreaders and individuals receiving
treatment, the subdivision of compartments to reflect levels of at-risk behavior or age demographics
and even the generalization of the transmission rate to a pair formulation [59].
As with the majority of compartmental models, our work has several limitations. To highlight
several, first, our model assumes a well-mixed (homogenous) population, which thereby disregards
the potential impact that heterogeneity may have on the transmission cycle and intervention. Naturally,
it follows that incorporating more realistic individual-level characteristics and mixing patterns would
enhance the accuracy of the predictions provided. Second, the calibration of our model relies on
reported chlamydia incidence from health authorities and estimates on the proportion of asymptomatic
cases. Implicit in this requirement are potential biases that may arise due to myriad treatment-seeking
behaviors among population groups such as those that mistrust medical personnel or age demographics
who experience greater social stigma from disease. Finally, the model formulation imposed a
parametric form of the duration of infection distribution. While the proposed distribution is flexible,
as it essentially can represent any function whose Fourier cosine series converges, further empirical
work is needed truly to determine the shape of the distribution.
5. Conclusions
In summary, our study evaluates a novel form of a compartmental model of chlamydia
transmission based on the quantity person-days of infection. Through our model, we better reflect
recent trends in chlamydia incidence in the U.S. based on the AIC score, relative to traditional
differential equation compartmental models. Given this outcome, our model projects a greater health
benefit from the upscaling of STI screening interventions than would be expected from traditional
approaches. By informing on the evaluation of STI screening interventions, in addition to the time
periods critical to the durations of chlamydia infection, our model has the capacity to uniquely
contribute to the wealth of knowledge needed to make informed decisions and thereby may aid health
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Mathematical Biosciences and Engineering Volume 20, Issue 9, 16131–16147.
officials in the construction of interventions to reverse increasing rates of STIs in the U.S.
Use of AI tools declaration
The authors declare they have not used Artificial Intelligence (AI) tools in the creation of this article.
Acknowledgments
The authors wish to thank Dr. Emelie Kenny for constructive feedback that greatly improved the
clarity of the work. SG was partially supported by the National Science Foundation Grant DMS-2052592.
Conflict of interest
All authors declare no conflict of interest in this paper.
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