Lecture 1
Here the goal is to familiarize you with the basic terminology of infectious disease epidemiology relevant for the spread of infectious diseases including the basic reproduction number (R0), herd immunity, index patient, endemic disease, epidemic disease, and pandemic.

An important concept in infectious disease transmission is the so-called transmission chain. A transmission chain is a sequence of transmission events from the origin to the secondary case. In this figure, one can see a transmission tree of Severe Acute Respiratory Syndrome (SARS) 2003 in Singapore where we can note the secondary cases generated by each infected case that was reported. We can see that only a few cases were able to generate most of the secondary transmission events.

This is an HIV transmission network that clearly shows the structure of transmission events. We can see here that each infected HIV person generates from 1 to 27 secondary cases. We can also see that most of these infected cases generate only a few secondary cases while a few of them generate many secondary transmission events.

A central quantity in infectious disease epidemiology is the so-called basic reproduction number, R0. This is defined as the average number of secondary cases generated by an infectious individual in a susceptible population. In this figure we can see that each infected person generates exactly two secondary cases for illustration purposes. Here R0=2 and the arrows denote the direction of transmission. In the bottom part of the figure we can see the generation number of the transmission events so in generation 1, there are a total of 2 cases while in generation 2 there are a total of 4 cases. We can see here how quickly an epidemic can grow with an R0 of 2.

Let’s look at R0 in more detail. In this example in the figure on the left, we can see that the first case in generation 0 generates two cases, in generation one each infected person generates two secondary cases. Therefore, taken these three infected individuals we can compute the average R0 as 2+2+2 dived by 3 infected cases, which equals 2. Therefore, R0=2 in this simple example.

However, it is more realistic to consider that some individuals are more susceptible, infectious or have higher contact rates in the population, and therefore we would expect to observe different numbers of secondary cases by each infected person. In this example in the figure on the left we can see that the index case in generation 0 generates 3 secondary cases. Then each of these 3 new cases generates 1, 1 and 2 secondary cases, respectively. We can see, therefore, that R0 can be computed by taking the average number of secondary cases by each infected individual.

Let’s compute R0 in this example. The first case generates 3 secondary cases. Each of the new cases generated 1, 1, and 2 secondary cases. Therefore, considering each of these 3 infected individuals we have an average R0 of 1.75.

By now you should have noticed that R0 needs to be greater than one in order to have an outbreak or an epidemic (e.g., to have sustained transmission events). In this example we have an index cases generating two secondary cases. Then each of the new cases generates 0 and 1 secondary cases, respectively. R0 is relatively low and very close to 1. If we compute the average R0 in this situation, we have 2 secondary cases generated in generation 0 and 1 and 0 secondary cases generated by the infected individuals in generation 1. Therefore, R0 equals one. In this situation it is not clear if the infection will continue spreading. If R0<1 then the infectious agent won’t spread very far.

In the SARS transmission chain figure that we showed you earlier, we do have an outbreak with an R0>1. In this situation we have an epidemic of SARS.

R0 can inform public health authorities whether an infectious agent will spread or not. R0 is the average number of new infections generated by an infectious individual in a completely susceptible population. Therefore, If R0<1 the infectious agent is not expected to spread in the population, but if R0>1 then we expect to see an outbreak or an epidemic.

R0 can be related to the impact of control interventions (e.g., via vaccination). As you know vaccination reduces the number of susceptible individuals in the population. Therefore, vaccination reduces the chances of infected individuals to generate secondary cases. If we are able to reduce R0 to a number less than one, then an infectious agent cannot spread in the population.

Another important concept in infectious disease epidemiology is herd immunity. Herd immunity is basically the critical fraction of the susceptible population that needs to be immunized/protected in order for the infectious agent not to spread in the population.

To date, many countries have been able to stop the spread of infectious diseases via vaccination. In particular childhood infectious diseases such as measles, mumps, and rubella have been controlled by vaccinating a large fraction of susceptible individuals in a population.

Index patient is the first recognized case in an epidemic or an outbreak. In this figure of the transmission tree of SARS in Singapore, we can see that Ms EM is our index patient. We note that the quick identification of the index patient has public health relevance for the control or emerging and reemerging infectious diseases.

Perhaps one of the most famous examples for an index patient is the so-known Typhoid Mary. Mary Mallon was a cook who spread typhoid to may people who ate her food. It is now recognized that she was responsible for a number of typhoid outbreaks transmitted through food.

Let me show you how an epidemic can bee seen over time. In the figure we can see that the Y-axis is the number of new infections, and the X-axis is time, which can be given in days, weeks or months depending on the infectious disease in question. The most important part here is how an epidemic can evolve over time. At the very beginning when the index patient is introduced into the susceptible population we have the so-called random effects. That is, this index patient is transmitting the infection to a few cases depending on R0. If R0 > 1 the infectious agent is expected to spread in the population, and therefore we expect to see an epidemic. The infectious agent will then grow exponentially fast in the population. Then the infectious agent will reach a peak as we can see in the figure. After that we expect to see a decline in the number of new cases because the number of susceptible have been depleted. After this decline in the number of new infections, we can expect this epidemic to cease/die out or perhaps we can expect that the number of new cases will reach an endemic state, which is an approximately constant level of new cases over time, or perhaps we can expect to see another epidemic depending on the infectious disease in question or the epidemiology of the infectious agent.

Let’s differentiate between endemic and epidemic diseases. For an endemic disease, the number of new cases is approximately constant over time. For the case of an epidemic, we can see a rapid increase in the number of new cases. That is, the number of new cases grow rapidly, reach a peak, and then decline. In this situation we are talking about an epidemic. In this figure we can see the impact of the 1918 influenza pandemic in terms of mortality over time. We can see that the 1918 pandemic generated an abrupt increase in number of cases, which was preceded by a relatively constant level of mortality.

A pandemic is a global epidemic. In this concept the dimension of space is introduced. When an epidemic affects the entire world, then we can talk about a pandemic. When an infectious agent affects a single county, city or area, then we typically talk about an epidemic taking place. In this figure we can see a number of sick people from the 1918 influenza pandemic that affected the entire world and generated from 20 to 100 million deaths.

Let’s quickly review the epidemiological concepts that we covered in this lecture.
R0 is the average number of secondary cases generated by a primary infectious individual in a susceptible population. If R0 >1 an epidemic is expected to occur while R0<1 cannot sustain an epidemic. Herd immunity is the critical fraction of the population that needs to be protected for the infectious disease agent not to spread in the population. The index patient is the first recognized case in an epidemic or an outbreak. Endemic disease occurs when the number of new cases is approximately constant over time. For the case of an epidemic, we can see a rapid increase in the number of new cases over time. Pandemic is a global epidemic.

Lecture2
By the end of this session you should understand another set of infectious disease epidemiology concepts including incubation period, latent period, case fatality rate, mortality rate, incidence, and prevalence.

Two important concepts are the latent and incubation periods. The latent period is the time that elapses from infection to becoming contagious or infectious in order for the individual to be able to transmit the infection to others. The incubation period is the time that elapses from infection to the appearance of symptoms in the individual. In the figure we can see that the latent period is defined based on the ability of the individual to transmit the infection to others while the incubation period is defined in reference to the appearance of symptoms.

Perhaps it is not surprising that latent and incubation period concepts are often confused. In the figure we can see that the latent period is defined based on the ability of the individual to transmit the infection to others while the incubation period is defined in reference to the appearance of symptoms. For instance for the case of influenza, the latent period is about 1-2 days while the incubation period is approximately 2 days. Research has shown that the latent period of influenza is about one day while the incubation period is typically two days. That is, individuals infected with flu can be able to transmit disease to others about 24 hrs. before the appearance of symptoms. As another example, in the case of HIV infected individuals have a latent period of just a few weeks before individuals can transmit disease to other individuals while the incubation period of HIV can be up to several years long.

Another two important epidemiological quantities are the mortality rate and the case fatality rate. Mortality rate is defined as the number of people who die of a disease in the entire population. For instance, if we say that 10% of a population died of plague then the mortality rate is then 10%. The case fatality rate is defined as the fraction of people who die of a disease among those who are infected. For example, the case fatality rate of pandemic influenza is about 5%. That is, 5% of the entire pool of infected individuals actually died from the disease.

For us to be able to estimate mortality rate and the case fatality rate, we would need to know those that uninfected in the population, those that are infected and recovered and those that got infected and died. Using these pieces of information we should be able to compute the mortality rate and the case fatality rate.

Let’s look at a specific example. In this population, in the overall yellow box, we can see that we have a total of 12 people. So our population size is 12. Out of those 12 people, 4 people got infected, and out of those 4 infected people, 2 people actually died from the disease.

Let’s go ahead and compute the mortality rate and the case fatality rate. To compute the mortality rate we divide the total number of people that died which is 2 by 12, which is the total population size. That gives us a mortality rate of 2/12=16.7%. Now, the case fatality rate is obtained by dividing 2 people that died by 4 total infected individuals, which leads to a case fatality rate of 50%.

Let’s review the computations of mortality rate and the case fatality rate. The mortality rate was obtained by dividing the total number of deaths by the population size while the case fatality rate was obtained by dividing the total number of deaths by the total number of infected cases. The case fatality rate can give us information on the risk of an individual dying from the infection. For example, in the case of rabies, which is transmitted to humans from bites from infectious dogs, skunks or foxes, the case fatality rate is pretty high. It is actually 50% or higher. The individual risk of dying from a bite of a rabid animal is actually very high. On the other hand, the mortality rate for rabies in the population is very low because the chances of the virus to be transmitted form a rabid animal to a person are very low so we expect to observe a low mortality rate. However, if this rabies virus could be able to mutate in a form that could be easily transmissible from person to person, then we could observe high mortality rates.

Other two important quantities in epidemiology are incidence and prevalence. Incidence is the number of new cases per unit of time (day, week or month) and is usually expressed as a fraction of the population. For instance, in the case of an ongoing influenza epidemic, if 200 influenza cases are reported today, then the incidence of influenza today is 200 cases this day. In the case of prevalence, it is the total number of people with the illness at a given point in time. It does not matter if the cases were generated today or 10 days ago, if the cases are still affected with illness then they are counted as prevalence. For example, the incidence of HIV/AIDS in the world is 2-3 million per year in the world, while the prevalence of HIV/AIDS is around 30 million people living with HIV/AIDS in the world.

We will now define several disease transmission routes including person-to-person, fecal-oral, and vector-borne that could include a resevoir or not.

It is critical to understand how infectious diseases transmit in populations. Once we know the mechanisms behind the transmission of an infectious agent, we should be able to devise effective intervention strategies and develop preventive measures. In summary, it is important to understand first how an infectious agent is transmitted in the population in order for us to find ways to halt its spread. To achieve this, we need to work in interdisciplinary teams that include engineers, anthropologists, educators, public health experts, etc.

Many infectious diseases are transmitted from person to person, which could involve indirect contact (close contact), direct contact (e.g., sexual intercourse), and droplet transmission. Droplets are small particles containing virus that can be suspended in the air and transmitted to other persons. Another indirect form of transmission is fomite transmission, which includes transmission via doorknobs –- virus particles are left behind in different objects such as tabletops and doorknobs by human contact. In order for us to prevent the spread of person-to-person infectious agents, it could entail the use of face masks, school closures, limiting public gatherings, quarantine (suspected infected cases are isolated), hand washing, and cough and sneeze etiquette.

Another route of transmission of infectious diseases is the fecal-oral. This means that the infectious agent is located in secreted feces of an individual, which are then transported in the form of small particles to food or water, which are then consumed by another individual. This is how the transmission cycle is closed. The fecal-oral route is responsible for the transmission of diseases such as cholera or salmonella and typically occurs in low-socioeconomic populations. In order to interrupt the transmission via fecal-oral route we need to place food hygiene laws in order to prevent food poisoning. That is why employees are required to wash hands in restaurants every time they go to the bathroom. For relevant disease control, we need to have clean/safe water through water sanitation and need to wash hands in order to kill infectious agents that are in our hands.

Several infectious diseases are transmitted via a vector and are known as vector-borne diseases. In order for these agents to be transmitted in the population, a vector is required to transmit the infection from an infected person to a susceptible individual or from a reservoir where the infectious agent could live happily. This is how vector-borne diseases are transmitted in a population.

The great majority of the world population is at risk of infection with vector-borne diseases such as dengue or malaria. By far it is a mosquito the responsible for over 90% of vector-borne disease transmission. For the case of dengue we have a mosquito that is responsible to transmit the dengue virus from person to person. For the case of malaria that is caused by the plasmodium parasite we have another type of mosquito capable of transmitting the malaria parasite from person to person. For control of dengue or malaria, it is necessary to prevent the infection from the mosquito by using barriers such as bed nets. More importantly it is more effective to control the mosquito population by eliminating the mosquito at the larva or pupa stage or as an adult flying mosquito. There is a great deal of research that is being carried out for the development of more effective intervention strategies for the control of vector-borne diseases particularly dengue and malaria.

Let’s review the epidemiological concepts that we covered in this session.

Incubation/latent period.
The latent period is the time that elapses from infection to becoming contagious or infectious in order for the individual to be able to transmit the infection. The incubation period is the time that elapses from infection to the appearance of symptoms in the individual.

Mortality rate/case fatality rate
Mortality rate is defined as the number of people who die of a disease in the entire population while the case fatality rate is defined as the fraction of people who die of a disease among those who are infected

Incidence/prevalence
Incidence is the number of new cases per unit of time (day, week or month) and is usually expressed as a fraction of the population. Prevalence is the total number of people with the illness at a given point in time.

Finally we also covered the main transmission routes for infectious diseases namely person-to-person, fecal-oral, and vector-borne.

Lecture3
I am particularly interested in problems in which the application of mathematical, statistical and computational tools could be useful in unraveling the transmission dynamics of infectious disease transmission and evolution. Here I will focus on my work related to the transmission and control of seasonal and pandemic influenza

First, I would like to tell you that influenza is a very dynamic virus, continuously changing over time to ensure its survival in the human population. Changes in the influenza virus can vary from small point mutations which are responsible for yearly influenza epidemics while major changes in the influenza virus composition are responsible for global epidemics of influenza (known as pandemics) which typically lead to substantial morbidity and mortality burden in the human population..
As the figure shows, the influenza virus has avian and swine reservoirs which are key for the evolution of the influenza virus. Transmission events of the influenza virus between the avian and swine reservoirs can lead to novel influenza viruses, which in turn could be be further recombined with human influenza to potentially generate completely new viruses with high transmissibility and pathogenicity to generate a human pandemic of great morbidity and mortality.

Influenza pandemics are global (world wide) epidemics. This figure shows the timing of emergence of pandemic viruses and their corresponding periods of circulation. By far the 1918 influenza pandemic has generated the highest death toll (20-100 million deaths) and 675000 deaths in the US alone.

During the 2009 A/H1N1 influenza pandemic, there was a sudden increase in the rate of severe pneumonia and a shift in the age distribution of patients with such illness, which suggested relative protection for persons who were exposed to H1N1 strains during childhood before the 1957 pandemic. In this figure we can see that pandemic mortality was concentrated in young adults while older adults enjoyed some protection to death. This mortality pattern is in contrast with the U-shaped mortality curve associated with seasonal influenza epidemics, shown in back and light gray in this figure. These findings suggested a rationale for focusing prevention efforts on younger populations.
The spatial-temporal distribution of A/H1N1 pandemic influenza reveal a three-wave pattern in the spring, summer, and fall of 2009 with substantial geographical clustering. The spring pandemic wave in April–May 2009 was mainly confined to the greater Mexico City area and other central states. The summer wave in June 2009 was limited to southern states, and ended soon after the start of the summer school vacation period on July 3, 2009. A third wave of widespread activity began in August 2009, coinciding with the return of students from summer vacations, and disease activity persisted until December 2009 throughout Mexico.

In this figure, one can readily see the three wave pandemic profile in Mexico, 2009. A total of 117,626 ILI cases were identified during April-December 2009 in Mexico, of which 30.6% were tested for influenza, and 23.3% were H1N1pdm-positive

There are 3 main goals of pandemic influenza mitigation: 1) To delay the impact of the epidemic to give time to public health authorities for the acquisition of antiviral medications and the development of a potential vaccine, 2) reduce the pandemic peak to diminish the stress imposed on hospitals and other health care facilities, and 3) reduce the overall pandemic attack rate

• The simplest epidemic model is the so-called SIR model, which classifies the population in 3 epidemiological states: susceptible, infectious, and recovered. This model is based on three assumptions: individuals mix uniformly in the population, The entire population is equally susceptible to infectious agent, and Individuals become infectious instantaneously after exposure to infectious agent.

In spring of 2009 in Mexico there were significant changes in the transmission rate according to school activity periods. By fitting a transmission model to daily influenza H1N1 case data, it is possible to quantify the relative change in mean transmission rate during the school closure intervention period. We estimated that the transmission rate was reduced by 29.6% (95% CI 28.9%–30.2%) during school closing period. The solid circles correspond to the data, the red solid curve corresponds to the model fit, and the blue lines are 95% confidence intervals of the model fit.

This figure shows the variability in reproduction number of seasonal influenza in the United States, France, and Australia. The red bar is the median reproduction number and the box is the interquaertile range.

Time series of monthly mortality rates coded as pneumonia and influenza (A), respiratory causes (B), respiratory and cardiac causes (C), and all causes (D), from January 2000 through April 2010, Mexico. Blue lines are observed mortality rates; black lines correspond to baseline rates predicted by a seasonal regression model; red dashed lines are upper 95% confidence interval of the baseline. Periods highlighted in gray mark seasonal influenza epidemic periods, while periods highlighted in orange highlight the 4 different waves of the A/H1N1 pandemic (spring 2009, summer 2009, fall 2009, winter 2010). Influenza dominant subtypes are indicated each season.

The 1918 influenza pandemic generated 675000 deaths in the US alone and anywhere from 20 to 100 million deaths in the world. This plot clearly shows the disproportionate impact of the 1918 influenza pandemic in the US, which reduced the average life expectancy of the US population by 11 years.

The 1918-1919 influenza pandemic swept the world in a series of pandemic waves. This figure shows the temporal evolution of the 1918 pandemic in Geneva, Switzerland in terms of the daily number of influenza hospital notifications. This figure clearly shows the spring-summer and fall pandemic waves.

This is the schematic representation of an SIR-type model to study the transmission dynamics of pandemic influenza. According to this model, the reproduction number is a sum of the contributions of the infectious class, the hospitalized class, and the asymptomatic class.

This figure shows the SIR model fit to the spring-summer and fall pandemic waves of the 1918 pandemic in Geneva, Switzerland. According to the model fit to the data, the reproduction number was 1.5 in the spring-summer wave and 3.8 for the fall pandemic wave.

We are currently carrying out efforts to unravel the impact of the 1918-1918 influenza pandemic in Latin America using historical archival data. In this figure we can see the weekly time series of respiratory mortality per 10,000 people in the city of Toluca, Mexico State, 1915–1920. Shaded areas highlight periods of high mortality, which correspond to the spring and fall pandemic waves in 1918 in Toluca.