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Revision as of 00:54, 1 November 2017

Epidemiological Model
of Chagas Disease

Introduction

We generated a model of the disease progression of Chagas disease in a human population. After equilibrium had been reached, we introduced our diagnostic device for congenital Chagas to assess the effectiveness of diagnosing congenital Chagas disease. We hoped to investigate the effect thatat curing infected newborns would have on the numbers of infected individuals in the whole population. the model parameters reflect the country of Bolivia, in which congenital Chagas disease is a major issue.

Methods

Technique, Assumptions, Parameters, Equations

Technique

Our model combines aspects of SIR and vector disease modeling to appropriately represent Chagas disease, which can be transmitted via a vector (Triatomine), horizontally (e.g. via blood transfusions and bodily fluids), and vertically (infected mother to child).

the parameters of our model reflect the country of Bolivia. the implementation of the diagnostic device, at t = 400 years, is modeled by a change in rIab, reflecting that 70% of infected newborns become diagnosed and treated, as compared to 0% prior to our diagnostic device.

Assumptions

1. All infants are tested with our diagnostic device
2. 70% of diagnosed infected infants successfully complete treatment (ref. E)
3. Birth and mortality rates in human and vector populations are fixed
4. Infected women in the acute phase cannot give birth
5. there is only one species of Triatomine (Rhodnius prolixus)
6. the impact of non-human host species (e.g. dogs, cats, and other synanthropic animals) is negligible
7. Frequency dependent transmission: 1 vector can infect only 1 host at a time
8. there is a fitness difference between healthy and infected vectors
9. the carrying capacity of the vector is 10x the carrying capacity of humans
10. Infants are cured instantaneously upon receiving treatment
11. No vector or transfusion control measures are undertaken in the duration of our model
12. No infants are diagnosed and treated prior to the implementation of our diagnostic device
13. the rate of movement from acute to chronic phase is not age-dependent

Parameters

Table 1. Parameters for Chagas Disease Epidemiological Model

Parameter	Variable Name	Value	Reference*
Carrying capacity of Triatomine	\(K_{b}\)	\(K_{p}~{\times}~10~(1{\times}10^{9})~Triatomine\)	A
Birth rate of Triatomine	\(r_{b}\)	\(36~births~Triatomine^{-1}~year^{-1}\)	A
Fitness of infected vector to give birth1	\(f_v\)	\(0.75\)	A
Mortality rate of vector	\(d_b\)	\(1.73~deaths~Triatomine^{-1}~year^{-1}\)	A
Probability of infection from human in acute phase	\(c_a\)	\(0.61\)	A
Probability of infection from human in chronic phase	\(c_d\)	\(0.2\)	A
Carrying capacity of humans2	\(K_p\)	\(1\times10^{8}~humans\)	–
birth rate of humans	\(r_{p}\)	\(0.023549~births~human^{-1}~year^{-1}\)	B
Mortality rate of humans	\(d_{n}\)	\(0.007353~deaths~human^{-1}~year^{-1}\)	C
Additional mortality rate of chronically infected humans	\(d_{d}\)	\(0.172647~deaths~human^{-1}~year^{-1}\)	D
Contact rate of vectors and humans	\(\beta\)	\(41\)	A
Probability of infection from vector to susceptible human	\(c_{vn}\)	\(0.00058\)	A
Probability of infection from infected chronic mother to child	\(c_{v_{c}}\)	\(0.049\)	E
Proportion of acute phase patients cured	\(r_{Ia}\)	\(0.65\)	F
Treatment completion rate for newborns	\(r_{I_{ab}}\)	\(0.7\)	E
Movement from acute phase to chronic phase	\(\delta\)	\(0.3\)	-
Immunity levels of treated adults3	\(\theta\)	\(\gt 0.03\)	–
Immunity levels of treated newborns5	\(\theta_{2}\)	\(\gt 0.03\)	–

^*See reference code at the bottom of the document.

¹0.75 is an estimate based on the suggested value of 0-1 by ref. A.

²An estimate; 10 times the current population of Bolivia.

³The immunity level is not currently known; Dr. Yves Carlier, an expert in Chagas disease, believes there is a high probability of immunity after the treatment of acutely infected Chagas patients. A parameter scan of our model indicates that our diagnostic device will be effective at lowering Chagas disease prevalence if the immunity value is greater than 0.03.

Equations

\(B\) = uninfected vectors

\(V\) = infected vectors

\(S\) = susceptible adults

\(I_{a}\) = infected adults in the chronic phase

\(I_{b}\) = infected babies in the acute phase

\(I_{c}\) = infected individuals in the chronic phase

\(R\) = immune adults

\(C\) = cured babies

\(D\) = death due to Chagas disease

\(Checked\) = tested babies

\(Rb\) = immune babies

\(Sb\) = susceptible babies

\(N = S + Ia + Ib + Ic + R\)

Differential Equations

Results

After our diagnostic device is implemented (at t = 400 years), there is a decrease [percent decrease] in the number of infected humans of all classes of infection: acute phase (Ia) [0.33%], chronic phase (Ic) [2.8%], infants (Ib) [71%], and total [2.7%]. 95% of the change is achieved within 141 years (5-6 generations) of implementation of our diagnostic.

Discussions

Assuming the implementation of our diagnostic device results in the diagnosis and subsequent treatment of 70% of infected newborns, there is a noticeable decrease in the number of acutely, chronically, and total infected humans in our model. This is likely a result of the decreased number of infectious newborns in the population. The treatment of newborns prevents their ability to infect others (horizontally or vertically) over the course of their life and may decrease the susceptible pool size – once treated, the individual is cured and immune for life. By implementing our inexpensive and easy-to-use diagnostic device on a large scale in the modeled population, we would be able to drastically decrease congenital cases of Chagas disease and thus the spread of the Chagas disease to the rest of the population.

Evaluation

The predictive value of our model is dependent on the accuracy of the many parameters considered. All parameter values were informed by research papers and credible websites published/updated within the last 10 years. There is, however, some uncertainty surrounding the parameters of vector fitness and immunity. A sensitivity analysis shows that the value of the fitness of an infected vector to give birth does not greatly affect the outcome of the model. Immunity rate has a larger impact, but a parameter scan indicated that our diagnostic device would be successful in lowering Chagas disease cases for an immunity rate value greater than 0.03 (corresponding to a 3% lower chance in getting infected again after successful treatment than a susceptible person who has never been infected). We consulted Dr. Yves Carlier, an expert in Chagas disease; he believed it was likely that treatment of Chagas disease in newborns would confer some immunity, strengthening our confidence in our device and model. The sensitivity analysis also demonstrated that the parameters whose values were most likely impact to the outcome of our model are the birth and death rates of humans. We are very confident in these parameters, which are taken from the World Bank database.

The assumptions we made in our model also contribute to its predictive value. We made the assumptions, stated above, in cases where there was insufficient data to include a parameter and, upon the recommendation of our supervisors, to limit the complexity of the model. Many of these are backed up by extensive research and literature. There are, however, a few assumptions that may limit the predictive accuracy of our model. These relate to biology, sociology, and treatment:

• Biology: Many animals that can transmit Chagas disease, including synanthropic animals and additional species of Triatomine, are not considered in this model. They were excluded for reasons of clarity and their comparatively small contribution to Chagas disease prevalence. The inclusion of these would likely increase the number of Chagas cases in our model.
• Sociology: Our model assumes that all infants are tested (but only 70% treated). While there are incentives to give birth in hospitals – as Dr. Cristina Alonso-Vega, the leader of the Program for National Control of Congenital Chagas in Bolivia (2004–2009) informed us – some women still deliver their babies at home. These newborns would have a lower likelihood of being tested for Chagas disease. Another factor that should be, but is not explicitly considered in our model, is the dependence of parameters on how rural/urban an area is.
• Treatment: We assumed that infants are cured instantaneously upon receiving treatment. This is not physiologically true – it takes 6 weeks in real life. We made the assumption, however, because 6 weeks is a negligible time with respect to the duration of our entire model (200 years).

Many of our assumptions are realistic at the time the model was created, but may change in the future. One example is the treatment completion rate of newborns (70%) (ref. E); we hope this number will increase in the future.

In the future, we could expand on our model by including more parameters and adjusting some of the assumptions discussed above. We would also continue to update parameter values to reflect progress in Bolivia.

Integration

The disease modeling has been informed by, as well as shaped, our integrated human practices. Designing this model prompted us to establish lines of communication with experts in Chagas disease (including Dr. Cristina Alonso-Vega and Dr. Yves Carlier) and mathematical biology (Dr. Michael Bonsall). It also played a role in our decision to create a leaflet for individuals living with Chagas disease – most of the mothers of infected children may not be able to obtain treatment and will thus remain in the chronically infected group. Our leaflet aims to educate these women, as well as other infected people, about what to expect when living with Chagas disease and how to protect others from infection.

References