Socioeconomic Status Affects Recovery Rate for Flu


If the effect of socioeconomic statuses on the recovery rate of the flu is considered, a revised SIR model with different recovery rates for the various socioeconomic groups can be created.

The typical SIR model includes many assumptions, allowing for a simple model. Important assumptions in the SIR model are that the transmission and recovery rates are fixed constants. Other assumptions include all individuals are the same age, have the same number of contacts with infected people, and have the same socioeconomic status. When socioeconomic status and its effect on recovery rate is considered, an SIR model showing different recovery rates can be made.

One risk factor for influenza is asthma. People with asthma have a greater chance of facing complications from the flu (1). According to a study, socioeconomic status was found to be negatively associated with asthma (2). Low socioeconomic status individuals often live in urban areas and are exposed to both indoor and outdoor pollution, leading to increased chances of asthma (2). This is important in considering the SIR model since people with asthma will more likely have a slower rate of recovery compared to the average.

The rate of recovery from the flu is also affected by the amount of rest taken. Low socioeconomic status individuals are more likely to not take as many days off as those with higher status (3). Many in the low socioeconomic group are also less likely to receive medical care and attention (4). With more stress on the body, the time for recovery may increase.

Those with higher socioeconomic status have greater access to health care and are not restricted in terms of medical attention or care by money. In addition, they are more likely to take days off from work. This means that those with higher socioeconomic status will be more likely to recover from a disease at a faster rate.

According to the simple SIR model (Figure 1), all individuals are assumed to have the same recovery rate. However, a revised SIR model (Figure 2) that takes into consideration three different socioeconomic statuses can show the different recovery rates in the various groups over time. If the average recovery rate is 5% for those with medium socioeconomic status, assume that the recovery rate is 1% in the low category and 9% in the high category. The recovery population in the three socioeconomic groups are not drastically different, but with greater differences in the recovery rate, the more different the recovery populations will be (Figure 3).

Figure 1. SIR model under the assumption all people have the same recovery rate

S’ = – beta * S * I, I’ = beta * S * I- gammaMed*I, RLow= gammaLow*I, RMed = gammaMed *I, RHigh = gammaHigh *I


Figure 2. Revised SIR model with recovery rates associated with socioeconomic status

beta= 0.00002; gammaLow = 0.01; gammaMed= 0.05; gammaHigh = 0.09;


Figure 3. Revised SIR model with recovery rates associated with socioeconomic status

beta= 0.00002; gammaLow = 0.005; gammaMed = 0.05; gammaHigh =0.5;

Although the revised SIR model takes into consideration the categories of socioeconomic status, the model is still very simplified. Limitations include that there are only three categories, while realistically, people fall within the spectrum. Other factors that can affect the outbreak of a disease include age, number of interactions, and environmental factors, all of which are not considered in this model.

The SIR model is simply a model and cannot predict exact numbers, but the disparity between the socioeconomic groups should be taken into consideration when modeling diseases.

  1. “Flu and People with Asthma.” Centers for Disease Control and Prevention. Centers for Disease Control and Prevention, 25 Aug. 2016. Web. 04 Nov. 2016. <>.
  2. Bacon, Simon. “Individual-level Socioeconomic Status Is Associated with Worse Asthma Morbidity in Patients with Asthma.” Respiratory Research. BioMed Central, 2009. Web. 04 Nov. 2016. <>.
  3. “Work, Stress, and Health & Socioeconomic Status.” American Psychological Association. APA, 2016. Web. 04 Nov. 2016. <>.
  4. Adler,  Nancy E.” Socioeconomic Disparities In Health: Pathways And Policies. “Project HOPE, 01 Mar. 2002. Web. 04 Nov. 2016. <>.

Selina Husain, Jasmine Pacheco-Ramos, Ayumi Mizuno

Who’s Next? Infection, Susceptibility, and The Age Pyramid

Randy Jones

Are you a frequent flyer? Whether for business or for fun, most of us have traveled somewhere internationally at least once in our lives. This increase in international travel completely changes how viruses and diseases spread. Whether you realize it or not, your susceptibility to certain illnesses is greatly affected by your age. These susceptibility differences within age groups can change the entire age distributions within the population of the country you are departing from or arriving at.

How can epidemiologists and researchers use susceptibility data to study changing population distributions within a country? One simple, but highly effective way is to use an SIR model, which places individuals into three different compartments:  susceptible, infected, and recovered. Unfortunately, most SIR models make the assumption that age is not relevant, and do not include age differences within their susceptible populations. So, when you hear about an epidemic on the news, how do you know what age groups are being affected by the disease–should you be more concerned about your own susceptibility or your 4 year old child’s? Researchers Sara Y. Del Valle, James M. Hyman, and Nakul Chitins make a case for including age structures in SIR models in their study, “Mathematical Models of Contact Patterns Between Age Groups For Predicting the Spread of Infectious Diseases.” They write, “There are clear age-dependent differences in susceptibility that must be taken into account when developing models that will guide public health policy.”

There are a number of age-specific factors that should be considered when predicting the spread of infectious diseases. Think about it. What is a common fear about walking into a children’s daycare center during the winter? You are almost guaranteed to be exposed to coughs and sniffles. Assortativity, an age-dependent factor in disease spread, implies that people are most often in contact with those of a similar age. Since children under five are still developing mature immune systems and have not been exposed to nearly the same number of viruses as older age groups, they tend to be far more susceptible to colds and flus. Or, a child may be more susceptible to certain infections than their parent because the parent has been exposed to the infection before, which results in residual immunity.

On the other side of the spectrum, according to the CDC, Center for Disease Control, “between 71 percent and 85 percent of seasonal flu-related deaths have occurred in people 65 years and older and between 54 percent and 70 percent of seasonal flu-related hospitalizations have occurred among people in that age group.” One reason aged people are more severely affected by viruses like the flu is because as we age, our immune systems produce fewer naïve T cells. These cells are like empty files in a file cabinet. The more viruses we are exposed to, the more naive T cells are filled up and become memory T cells, which help your body remain resistant against viruses you have already come into contact with.

Considering these age-dependent factors influence the dynamics of epidemics, we sought to incorporate them into our SIR model; at the same time we hope to better understand how differences in age-structure susceptibility affect the age distributions of a country’s population. We took a basic SIR model and modified it to account for four age groups. We created three SIR models, each containing four age dependent plots and one age independent plot. Each model uses identical data with the exception of the susceptibility rate and the population distributions outlined below. 

The following assumptions were considered in generating each model:  Country A assumes a uniform population distribution (ie. developed country), while Country B assumes a typical pyramid distribution (ie. a developing country)  and Country C assumes an inverse pyramid population (ie. similar to what one might see in the E.U.)

Population size: 100,000


The figure below provides an model of what our three population distribution trends resemble:

The graphs below show that all age groups in each population distribution vary greatly, affecting the ratio of those susceptible, infected, and recovered far more than the static rates in which each group is infected.


With the same number of people in each of these populations, even when taking into account the differing susceptibilities between populations, the SIR models of the whole population don’t differ in any visually significant way. The population distributions don’t change the number of people infected or the rate of those infections, but they can greatly alter the probability of who will be next. In this case, the answer is clear and intuitive; whichever is the most populous group will most likely contain the next victim of infection.


So watch out baby-boomers!

– Abigail Moore, Sara Van Cor, Tess Abbot

Additional Material:

SIR Models of Separate Age Groups in a Uniformly Distributed Population



SIR Models of Separate Age Groups in a  Developing Population




SIR Models of Separate Age Groups in an Developed Population




CDC. (2016, August 25). What you should know and do this flu season if you are 65 years and older. Retrieved November 6, 2016, from Influenza(Flu), http://

Del Valle SY, Hyman JM, Chitnis N. MATHEMATICAL MODELS OF CONTACT PATTERNS BETWEEN AGE GROUPS FOR PREDICTING THE SPREAD OF INFECTIOUS DISEASES. Mathematical biosciences and engineering : MBE. 2013;10(0):1475-1497.

IMMUNE SYSTEM: Can your immune system still defend you as you age? (2011, December 13). Retrieved November 6, 2016, from National Institute on Aging,

Laskowski, M. (2011). The impact of demographic variables on disease spread: Influenza in remote communities. Scientific Reports, 1, 105.

The Influence of Prediction Time on the Rate of Vaccination and Infection by Influenza

By: Tingshan, Jessica, and Amalia

The CDC characterized last year’s flu as having “extremely high hospitalization rates” for both children and older adults (1). To keep that number from climbing many citizens opt to get vaccinated against the unforgiving grip of this seemingly benign disease. There are 319 million disease carrying vectors in the United States and if you are one of the 29 million without health insurance, the prospects of getting this disease are terrifying (2). Unfortunately, getting health insurance isn’t a walk in the park either. In 2015, 43 million people were below the poverty line in the United States (3). Obamacare can be up to $800 a month, which can be more almost 50% of the monthly income of many Americans (4). Unless our capitalist government revises its regime, that heart wrenching number of people without health insurance will likely only ascend.
Particular strains are more deadly than others. The CDC reports that, “Seasons during which influenza A (H3N2) viruses predominate typically have higher rates of hospitalizations and more deaths, particularly among older people and children (5).” So, let’s say that last year there was an outbreak of H3N2. Now, this year there’s rumor of a strain very closely related to H3N2 that is mercilessly sweeping the nation, deemed H3llN0. It would be ideal to use the data collected from the H3N2 infection that took place during the past season and apply it to form a hypothesized SIR model for the incoming H3llN0 mutated strain.
Our models are based off of this idea, we began with “model 1,” or the model with a constant population of people who receive vaccinations. We included this model in the series for the sake of comparison, and the recovery rate is linearly dependent on the vaccination population (Figure 1).

Screen Shot 2016-11-04 at 5.30.22 PM

The next model called “model 2,” has useful data gathered from the past hypothetical H3N2 outbreak, with the infection rate proportional to the rate of vaccination (Figure 2). We focused on the infection rate from last year’s H3N2 outbreak 14 days after the initial infection because Day 14 of model 2 reflects a period of time where the infection rate was comparatively higher than it was at the beginning of the epidemic. So, to predict the H3llN0 upcoming outbreak, in model 4, the rate of vaccination on day one is proportional to the rate of infection during day 14 of model 2 (Figure 2). Starting the vaccination rate of model 4 at that point ensures that the projected estimate of the amount of people who should receive vaccinations would be more than sufficient. To reiterate, the estimate of people who should receive vaccinations on each day in the upcoming outbreak is based off of the number of those infected 14 days later from a similar epidemic that took place in the past. Model 3 (Figure 2) is based on the same premise as model 4; however the vaccination rate on day one is proportional to the rate of the infected population on day seven of model 2. In Figure 2, we used a vaccination rate of 1%, which means that 1% of the infected population would get vaccinated per day. This rate was arbitrarily assigned and when it was used it demonstrated the hypothesized results– a decrease in the number of people within the infected population.

Figure 2: Models 2-4 using a vaccination rate of 0.01 or 1% of the infected population. (A) This shows Models 2-4 within one graph (Model 2 in blue, Model 3 in green, and Model 4 in red). (B) An enlarged image of the peak of infection during the influenza vaccination. For Models 2-4, the peak of infection occurs at Day 48, but they have decreasing numbers of infection, as expected (Model 2- 2521 infected persons, Model 3- 2423 infected persons, Model 4 – 2330 infected persons). These models were generated using MATLAB Software.

The goal of this series of models was to see the impact of the prediction time on the rate of infection. Prediction time, in the case of our model series, refers to the selected timeframes of each model. In all models, the peak of the epidemic occurs approximately at the same point in time. The result of the models was that the longer the prediction time, the lower the infected population. In the third and fourth model, more people were vaccinated than in the second model. This logically makes sense because we increased the prediction time and consequently the vaccination rate was increased relative to the second model. We want to be cautious to not be overzealous with our results. We expect there to be a non-linear relationship between the prediction time and vaccination population, however we remain unable to definitively conclude that statement because the results gathered from this model series are highly population dependent.

Works Cited
Davlin, S. L. (2016). Influenza Activity—United States, 2015–16 Season and Composition of the 2016–17 Influenza Vaccine. MMWR. Morbidity and mortality weekly report, 65.
Barnett, J. C. & Vornovitsky. (2015). Health Insurance Coverage in the United States: 2015. United States Census Bureau. Retrieved from
Proctor, B.D., Semega, J.L., Kollar, M.A. (2016). Income and Poverty in the United States:2015. United States Census Bureau. Retrieved from
Vashi, S. & Hernadez, S. How much will you pay for Obamacare? CNN Money. Retrieved from
Appiah, G. D., Blanton, L., D’Mello, T., Kniss, K., Smith, S., Mustaquim, D., … & Bresee, J. (2015). Influenza activity-United States, 2014-15 season and composition of the 2015-16 influenza vaccine. MMWR. Morbidity and mortality weekly report, 64(21), 583-590.
Frequently Asked Flu Questions 2016-2017 Influenza Season. (2016). Centers for Disease Control and Prevention. Retrieved from
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The Effects of Chronic Obstructive Pulmonary Disease (COPD) on the Risk and Recovery Rates of Influenzae


Chronic Obstructive Pulmonary Disorder (COPD) is a group of conditions consisting of a number of respiratory defects that result in an obstructed airway (Wheaton et al., 2015). In this study, we explored the effects of COPD on infection rate and recovery rate of influenza. COPD weakens the respiratory system and tissues with symptoms like chronic cough and sputum production (Wheaton et al., 2015). Because of these effects of COPD, the influenza virus can infect lung tissues easier, increasing the susceptibility of people with COPD to the influenza virus. In addition, once infected with the influenza virus, people with COPD will recover slower than those without a chronic respiratory condition.

It was found in 2013 that approximately 6.4% of the U.S. population (including the District of Columbia and two U.S. territories) reported being diagnosed with COPD by a healthcare professional (Wheaton et al, 2015). This would be about 15.7 million U.S. residents in 2013 (Wheaton et al., 2015). It was also found that 10.6% of viral respiratory infections of those that have COPD are due to influenza viruses (Kwak et al., 2016). Several studies, from 2012-2013, have shown that once infected with influenza, patients that also had COPD had a slower and longer recovery rate than those without the disorder (Kwat et al., 2013). In order to model the transmission of and recovery from influenza for both a COPD and normal population, the SIR model was employed.

We modified the SIR model to account for the differences in infection/recovery rates of COPD population. For simplification purposes, we kept our total population constant by assuming there were no births and that all influenza and COPD cases were nonfatal.We subdivided the S (susceptible), I (infected), and R (recovered) groups into two subcategories (without COPD and with COPD) and supposed that within these subcategories everyone had the same infection/recovery constants (we did not take into account age, health, and other variables). People with COPD have a higher influenza infection rate than the non-COPD population. Hence, we used two different infection constants (a and b). Similarly, the infected population with respiratory diseases has a smaller recovery constant (m) than the non-COPD infected group (k). As shown in the differential equations below, the rates of change of the SIR groups are different for the COPD and non-COPD subdivisions.

SRI model

The resulting plot from the SIR model showed that having COPD affects the transmission of and recovery from influenza. We were able to see this by comparing the behavior of the graphs in the model’s two main subcategories – with and without COPD. Our initial conditions for susceptible and infected people with COPD were small numbers, causing the graphs of the COPD subcategories to be close to the x-axis. By zooming in on the plot to focus on the COPD graphs, we were able to compare the graphs more easily. Looking at the graphs for the number of infected people with COPD compared to without COPD showed that the number of people infected with influenza increases at a higher rate among people with COPD. Additionally, the recovery time for people with influenza is longer for those who also have COPD. We can see this on the plot because the graph of recovered people with COPD rises at a slower rate than the graph of recovered people without COPD. Comparing the graphs of the subcategories of the model allows us to see that how the rates of transmission and recovery are different for people with and without COPD.

SRI graphs One way in which we could’ve made the model more specific is by modifying it on a scale of the U.S population for which real date for influenza transmission and recovery in people with COPD indeed exist, but once we tried it, we saw that that model was not resulting in anything. The results of our model with smaller numbers, however, confirm that people with COPD are indeed more susceptible to getting influenza in a given season, and that once they have it, they also recover at a slower rate. This is of course, due to the fact that COPD already severely compromises their immune system, making it more vulnerable.


Kwat, Hyun Jung, D. W. Park, J. E. Kim, M. K Park, G. W. Koo, T. S. Park, J. Y. Moon, T. H. Kim, J. W. Sohn, H. J. Yoon, D. H. Shin, and S. H. Kim. “Prevalence and Risk Factors of Respiratory Viral Infections in Exacerbations of Chronic Obstructive Pulmonary Disease” The Tohoku Journal of Experimental Medicine, p. 131-139. October 05, 2016.

Wheaton, Anne G., T. J. Cunningham, E. S. Ford, and J. B. Croft. “Employment and Activity Limitations Among Adults with Chronic Obstructive Pulmonary Disease- United States, 2013” Center for Disease Control and Prevention. 64(11);289-295, March 27, 2015.


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