13-infectious_diseases.qmd

# Introduction to Infectious Diseases {#sec-13-infectious_diseases}

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Learning Objectives
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-   Learn about the dynamics of infectious diseases and their impact on
    human health
-   Understand the role of mathematical models in predicting infectious
    disease outbreaks
-   Explore the components of infectious disease models and their
    implications
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> **"Several infectious diseases are emerging and threatening human
> health worldwide. The burden of infectious diseases is undeniably a
> global issue, causing millions of deaths annually."[@santangelo2023]**

The advent of machine learning\index{Machine learning} (ML) has
revolutionised the field of **infectious disease
research**\index{Infectious disease} by providing robust tools for
predicting outbreaks and understanding the dynamics of spread. In this
section, we will enhance our understanding of these diseases and look at
the effects on Disability-Adjusted Life Years
(DALYs)\index{Disability Adjusted Life Years
(DALYs)} by applying **machine learning** and **data
visualisation**\index{Data visualisation} techniques learned in previous
chapters (@sec-05-machine_learning and @sec-09-data_visualisation). To
further improve the knowledge of the impact of infectious diseases on
global health\index{Global health}, we will explore how integrating ML
models can improve the accuracy\index{Accuracy} of disease
burden\index{Disease burden} estimations and provide valuable insights
into the impact of infectious diseases on public health.

## Infectious Diseases the Invisible Enemies

Emerging infectious diseases are a global concern, causing millions of
deaths annually. Understanding their behaviour and predicting outbreaks
is fundamental not only for public health but also for advancing
prediction techniques that can be applied in other fields.

**Microorganisms**\index{Microorganisms}, including
**bacteria**\index{Bacteria} and **viruses**\index{Virus}, adapt and
evolve at a rate much faster than humans. For example, the generation
time for bacteria can be as short as 20–30 minutes, while viruses can
replicate in even shorter time frames. This rapid adaptation allows
**pathogens**\index{Pathogens} to evolve quickly, developing resistance
to treatments and evading the **host**'s immune system.

Infectious diseases follow a multi-stage progression that begins when
the infective agent, whether **viral**, **bacterial**, or **parasitic**,
begins to thrive and multiply throughout the body[@broemeling2021] and
the process of infection starts. The rate at which the pathogen
proliferates varies significantly depending on the type of organism
involved. Each infectious disease has a unique **incubation
period**\index{Incubation period}, which is the interval between the
initial establishment of the pathogen in the host and the onset of
symptoms.

The incubation period can range from a few hours to several months,
influenced by factors such as the pathogen's growth rate, the host's
immune response, and the route of transmission. For example, the
incubation period for the **influenza virus**\index{Influenza virus} is
typically 1 to 4 days, whereas for diseases like **hepatitis
B**\index{Hepatitis}, it can be as long as 6 months. Understanding the
incubation period helps in identifying the time frame for potential
exposure.

Several factors influence an individual’s susceptibility to infection,
including:

-   Infection dose (quantity of invading germs)
-   Virulence (the ability of the organism to cause disease)
-   Immune status (the condition of the body's immune system)
-   Transmission route (contact with the source of infection for
    contagious diseases)

![Pathogens and humans have co-evolved over centuries, each adapting in
response to the other. This ongoing adaptation shapes the future of
health and
disease.](images/13_adaptation.png){#fig-adapt_virus
fig-align="center" fig-alt="Who adapts to whom? - (AI generated image)"
width="347"}

**Viruses**\index{Virus}, word derived from the Latin word for
**"poisonous substance"**, are intracellular parasites that can only
replicate within living host cells. Their sizes range from 20 to 400 nm
in diameter and can only be observed with an electron microscope.
Outside of a living cell, a virus is a dormant particle of various
shapes. Once inside a cell, it replicates, often killing the cell or
altering its functions.

The following seven diseases are all caused by an infectious agent such
as virus or bacteria, generally cause acute symptoms, ranging from mild
to severe, and require prompt medical attention to prevent complications
and further spread:

1.  [Acute Respiratory Infection
    (ARI)](https://www.ncbi.nlm.nih.gov/books/NBK11786/)\index{Acute Respiratory Infection
    (ARI)}
2.  [Covid-19](https://en.wikipedia.org/wiki/COVID-19)\index{COVID-19}
3.  [Dengue](https://en.wikipedia.org/wiki/Dengue_fever)\index{Dengue}
4.  [Influenza/Influenza-Like Illness
    (ILI)](https://en.wikipedia.org/wiki/Influenza)\index{Influenza/Influenza-Like Illness
    (ILI)}
5.  [Malaria](https://en.wikipedia.org/wiki/Malaria)\index{Malaria}
6.  [West Nile
    Virus](https://en.wikipedia.org/wiki/West_Nile_virus)\index{West Nile Virus}
7.  [Zika](https://en.wikipedia.org/wiki/Zika_fever)\index{Zika}

These diseases are transmitted through various means and can be grouped
by **transmission methods**\index{Transmission methods !}:

-   **Vector-Borne**\index{Transmission methods ! vector borne}: Dengue,
    Malaria, West Nile Virus, and Zika are primarily spread through
    mosquito bites.
-   **Respiratory
    Droplets**\index{Transmission methods ! respiratory droplets}: ARI,
    COVID-19, and Influenza/ILI are transmitted via respiratory droplets
    when infected individuals cough or sneeze.

## Mathematical Models for Infectious Diseases

The application of mathematical models to infectious diseases dates back
over a century, with significant contributions from pioneers such as
*Kermack*\index{Kermack} and *McKendrick*\index{McKendrick}, who
established the foundations of the subject[@keeling2009]. Their work
introduced the concept of categorising individuals based on their
epidemiological status: **susceptible**\index{Susceptible},
**infected**\index{Infected}, and **recovered**\index{Recovered}.

### The SIR Model

One of the simplest and most fundamental epidemiological models, the
**SIR model**\index{Susceptible Infected Recovered (SIR)}, to which we
had a quick look in the previous chapters (@sec-05-machine_learning and
@sec-06-techniques), is based on these three compartments and uses a
system of differential equations\index{Differential equations} to
describe how individuals move between these compartments based on
**infection rate**\index{Infection rate} and the **recovery
rate**\index{Recovery rate}. These parameters help predict the
epidemic’s progression\index{Epidemic}, showing how the number of
susceptible individuals decreases as the number of infected individuals
increases, eventually leading to recovery and a decline in new
infections, as shown in @eq-sir-model-theory.

More complex models, includes:

-   **SEIR Model**\index{Susceptible Exposed Infected Recovered (SEIR)}:
    This model introduces an exposed (E) compartment, which represents
    individuals who have been infected but are not yet infectious. This
    compartmentalization is particularly useful for diseases with
    significant incubation periods (e.g., COVID-19). Practical
    applications are in @sec-05-epidemic-x and @sec-14-modelling-covid19
    .
-   **SIS Model**\index{Susceptible Infected Susceptible (SIS)}: In this
    model, individuals who recover from infection do not gain lasting
    immunity, meaning they return to the susceptible class and can
    become reinfected.
-   **MSIR
    Model**\index{Maternal Susceptible Infected Recovered (MSIR)}: In
    some diseases, such as measles\index{Measles}, maternal antibodies
    provide temporary immunity\index{Immunity} to newborns. The M
    (maternal immunity)\index{Maternal Immunity (MI)} compartment is
    used in such cases.

## Components of Infectious Disease Models

1.  **Infection Rate**\index{Infection rate}: This parameter, often
    denoted as $\beta$ (beta), controls how quickly the susceptible
    population becomes infected. It depends on factors such as contact
    rate and the probability of transmission per contact. It is the rate
    at which individuals move from the susceptible compartment to the
    infected compartment. The infection rate is proportional to the
    product of susceptible and infected individuals[@kolokolnikov2020].

$$
\beta = \text{Contact Rate} \times \text{Probability of Transmission per Contact}
$$ {#eq-infection-rate}

2.  **Recovery Rate**\index{Recovery rate}: Denoted by $\gamma$ (gamma),
    this defines the rate at which infected individuals recover and
    either gain immunity or become susceptible again (depending on the
    model). The average duration of infection is the reciprocal of the
    recovery rate.

$$
\gamma = \frac{1}{\text{Average Duration of Infection}}
$$ {#eq-recovery-rate}

3.  **Incubation Period**\index{Incubation period}: In models like SEIR,
    the incubation period is the average time that exposed individuals
    take before they become infectious. This is a critical factor in
    diseases like COVID-19 and Ebola\index{Ebola}. The incubation period
    is the reciprocal of the rate at which individuals move from the
    exposed compartment to the infected compartment. $\sigma$ is the
    rate at which individuals move from the exposed compartment to the
    infected compartment.

$$
\text{Incubation Period} = \frac{1}{\sigma}
$$ {#eq-incubation-period}

4.  **Reproduction Ratio (**$R_0$)\index{Reproduction Ratio (R0)}: A key
    metric that indicates the **average number of secondary cases
    generated by one infectious individual in a fully susceptible
    population** is the **basic reproduction ratio (**$R_0$). This value
    is calculated using the formula in @eq-r0. $\beta$ is the
    transmission rate and $\gamma$ is the recovery rate. As the ratio of
    the transmission rate to the recovery rate, $R_0$ provides a measure
    of the disease's ability to spread.

$$
R_0 = \frac{\beta}{\gamma}
$$ {#eq-r0}

In summary, the SIR model is a simple yet powerful tool for
understanding the dynamics of infectious diseases. By tracking the
movement of individuals between susceptible, infected, and recovered
compartments, the model can predict the course of an epidemic and help
public health officials make informed decisions about disease control
measures. The value of $R_0$ determines the epidemic
**threshold**\index{Threshold}:

$$
\text{If } R_0 \left\{\begin{matrix}
 \begin{aligned}
 >1 = &  \text{ Epidemic}\\
 <1 = & \text{ End of Infection Transmission}
 \end{aligned}
\end{matrix}\right. 
$$ {#eq-r0-threshold}

To accounts for changes in the population's immunity, the **effective
reproduction number (**$R_{eff}$)\index{Effective
Reproduction Number (Reff)} is calculated on a susceptible population
which is not completely susceptible, and value of $R_{eff}$ results less
than $R0$ due to the presence of immune individuals in the population.

Another critical concept in infectious disease is the **herd
immunity**\index{Herd immunity}, which refers to the indirect protection
from infectious diseases that occurs when a large percentage of a
population becomes immune to the infection, either through vaccination
or previous infections. The herd immunity is reached when the effective
reproduction number is less than 1, and the disease stops spreading.

A related and dynamic measure is the force of infection ($\lambda$)\index{Force of infection}, which represents the per capita rate at which susceptible individuals acquire the infection. The force of infection depends on both the infection rate and the number of infectious individuals in the population. As immunity expands, the number of susceptible ($S$) declines, reducing the value of $\lambda$ and lowering the risk of infection. This decline in the force of infection reflects the mechanism by which herd immunity slows and eventually stops the spread of disease.

The SIR model shows the dynamics of an epidemic by looking at how it
grows and eventually declines. Initially, the number of cases rises
exponentially, leading to a peak, but as the susceptible population
start reducing in number due to various factors, the growth rate slows
with subsequent decline.

## Advancements and Extensions

Mathematical modelling has evolved to include more complex factors such
as age structure, stochasticity, and spatial dynamics. Age-structured
models, for example, consider how different age groups interact and
contribute to the spread of diseases, which is particularly important
for diseases like measles or COVID-19. Stochastic models account for
random events that can influence the course of an epidemic, such as the
introduction of the disease into a new population.

The use of machine learning algorithms such as **decision
trees**\index{Decision trees}, **random forests**\index{Random Forests},
**support vector machines**\index{Support Vector Machines (SVM)}, and
**deep-learning networks**\index{Deep Learning
Networks} such as **Long Short-Term Memory
(LSTM)**\index{Long Short-Term Memory (LSTM)} models, effectively
improve the identification of patterns and trends that may not be
obvious with mechanistic models. These models are able to improve
prediction accuracy working smoothly with large datasets.

Combining models and data sources enhances prediction accuracy, various
models and techniques can be applied to reduce bias and the risk of
overfitting. For instance, **ensemble
learning**\index{Ensemble learning} combines the predictions of multiple
models to improve accuracy. In this context, we will explore how machine
learning can predict infectious disease outbreaks\index{Outbreak} and
their impacts on human health, ultimately aiming to reduce the burden of
disease.

Another significant aspect to consider is the emerging use of **transfer
learning**\index{Transfer learning}, which involves applying knowledge
gained from one predictive task to another. This approach is especially
useful when data are limited and models need to be adapted. Although
relatively under-explored in infectious disease research, transfer
learning holds significant promise for improving predictions in areas
with scarce data. By leveraging information from related tasks, this
technique can enhance model performance, leading to more accurate and
reliable predictions in public health scenarios [@roster2022].

## The Impact on DALYs

To understand the magnitude of infectious diseases impacts on
DALYs\index{Disability Adjusted Life Years (DALYs)}, we can simply
consider the DALYs rate of change. The percentage change in total DALYs
and DALYs due to infectious diseases, in general or for a specific
infective virus such as COVID19, allows us to assess the impact on the
overall burden of disease\index{Burden of disease}. In the case of
COVID19 for example, the percentage change in DALYs due to COVID19 can
explain how this virus affected global health and produced excess
mortality and morbidity.

$$
\text{Percent change in DALYs} = \frac{\text{DALYs due to Infectious Diseases}}{\text{Total DALYs}} \times 100
$$ {#eq-daly-change}

Where the $DALYs = \sum_{i=1}^{n}{(YLD_i + YLL_i)}$, $YLD$ and $YLL$ are
the years lived with disability and the years of life lost respectively.

This percentage change provides a measure of the impact of infectious
diseases on the overall burden of disease. The DALYs due to infectious
diseases can be calculated as the sum of the DALYs for each disease, and
the total DALYs can be calculated as the sum of the DALYs for all
diseases. The percentage change in DALYs due to infectious diseases can
then be calculated as the ratio of the DALYs due to infectious diseases
to the total DALYs, multiplied by 100.

Furthermore, the use of machine learning\index{Machine learning} models
used to predict the variation of number of DALYs due to infectious
diseases over time can be a valuable tool to understand the impact of
infectious diseases on global health. Two approaches can be valued:

1.  DALYs as a function of the **socio-demographic index
    (SDI)**\index{Socio Demographic Index (SDI)}: A composite index of
    the average income per person, educational attainment, and total
    fertility rate. The model function can be expressed as: $$
    DALY_{id}= f(SDI)+\epsilon
    $$ {#eq-daly-sdi} where is the number of $DALYs$ is the response
    variable, $SDI$ the socio-demographic index acting as predictor,
    $f(.)$ is the function that relates the number of DALYs to the
    socio-demographic index, and $\epsilon$ is the error term.

2.  DALYs as a function of the **human development index
    (HDI)**\index{Human Development Index
    (HDI)}: A composite index of life expectancy, education, and per
    capita income indicators. The model function can be expressed as: $$
    DALY_{id}= f(HDI)+\epsilon
    $$ {#eq-daly-hdi} where is the number of $DALYs$ is the response
    variable, $HDI$ the human development index where is the number of
    $DALYs$ is the response variable, $HDI$ the socio-demographic index
    acting as predictor, $f(.)$ is the function that relates the number
    of DALYs to the socio-demographic index, and $\epsilon$ is the error
    term. Big data analytics with machine learning analysis are used to
    classify the patterns of global disease burden by human development
    index (HDI) to have a better understanding of DALYs caused by
    infectious diseases such as COVID19 given different levels of HDI.

This can help us to understand the trends and patterns of infectious
diseases and their impact on global health.