Análisis Interno y Externo de la Empresa

Some keywords within the definition of epidemiology are elaborated below to highlight some of the important guiding principles in epidemiology:

 Study, concerns surveillance, observation and research of health related events;

 Distribution, refers to the analysis of the frequency and patterns of health related events over space and time;

 Determinants, concerns the factors that bring about a change in a health condition, such as biological, geographic, social, cultural, economic or political factors;

 Health-related states or events, refers to activities associated with disease states, such as outbreaks, causes of death, preventative programs and health and social services; and

 Application, concerns the overarching goal of epidemiology, namely to promote, protect and restore public health.

When undertaking epidemiological research, two approaches are used, namely descriptive epidemiology and analytical epidemiology. Descriptive epidemiology concerns the study of the occurrence of a disease and health-related characteristics (Porta 2014). These include basic characteristics such as age, gender, occupation, social class and geographic location. People, time and place thus play an important role in descriptive epidemiology.

In contrast, analytical epidemiology concerns the testing of the validity and strength of causal links between the observed patterns and the factors which affect the risk of disease (CDC 2012). In short, whereas descriptive epidemiology is used to generate hypotheses about disease occurrence and dynamics, analytical epidemiology is used to test these hypotheses (CDC 2012).

Jewell (Jewell 2004) further states the epidemiological study of the disease process would focus on answering two questions, namely:

 Which risk factors are strongly associated with the induction, promotion and expression of a disease; and

 Which risk factors influence the length of induction, promotion and expression periods? These research questions, in addition to risk factors relating to disease causation (previously mentioned in §2.1.4) link closely to the considerations and approaches of descriptive epidemiology.

In conclusion, the importance of viewing disease causation as a complex interaction of various risk factors may be useful when designing and adopting holistic modelling approaches. The guiding principles of epidemiology serve as a good starting point to approach disease dynamics from a high- level perspective and study of factors and interactions which potentially affect disease transmission.

This remainder of the section contains background information on a selection of modelling parameters and terms that are key to understanding the considerations which form part of the infectious disease modelling and analysis process.

Herd immunity

The protective phenomenon observed when a high proportion of hosts in a population are immune against a disease, which in turn protects the few remaining susceptible individuals within the population, is referred to as herd immunity (Altizer et al. 2006). This phenomenon is typically achieved by means of prophylactic (i.e. preventative) vaccination or as a result of immunity following previous recovery from an infection.

The law of mass action

According to Grassly and Fraser (2008), the mass action law states that “the rate at which individuals of two types contact one another in a population is proportional to the product of their densities.” What this law implies is that a pattern of fast initial growth is typically associated with disease outbreaks, followed by a typical decrease in the rate of new infections once the number of infected individuals surpass the number of susceptible individuals. This phenomenon typically leads to the bell-shaped curve associated with epidemics (Grassly & Fraser 2008).

Contact mixing pattern

When modelling the spread of disease between individuals in a population, the manner in which these individuals have contact with each other is an important aspect of the modelling considerations and assumptions. The disease transmission mode may greatly influence these contact assumptions, as close proximity is required for diseases which spread by means of direct contact, whereas diseases which spread primarily by vectors such as mosquitoes might not be as dependant on contact-related assumptions.

The most common mixing pattern employed by default is homogeneous (i.e. random) mixing, which assumes that each individual has the same average rate of contact with any other individual (Mishra et al. 2011). This implies that individuals have uniform contact with each other and an equal probability of having contact with any other individual. The use of this assumption greatly simplifies mathematical modelling applications and is very commonly used.

In contrast, when adopting heterogeneous (i.e. non-random) mixing patterns in the modelling approach, the modeller allows for some individuals to have a higher average contact rate than other individuals, as a result of social, spatial or behavioural differences (Mishra et al. 2011). Some examples of heterogeneous mixing patterns include:

 Assortative mixing, when contact between individuals of similar groups (e.g. social or certain age groups) are more likely to occur; and

 Disassortative mixing, which in contrast to assortative mixing, is when contact between individuals of dissimilar groups are more likely to occur.

Transmission probability parameter

The transmission parameter 𝛽 is used to quantify the probability that an infected host will transmit the disease to a susceptible host, given sufficient contact occurs between individuals (Mishra et al. 2011). This parameter forms an important part in quantifying the infectiousness of a disease, as it is one of the primary parameters which determine the probability of infection.

Basic reproduction number

The basic reproduction number 𝑅𝑜 is the average number of secondary disease cases typically caused by an infected individual (Chowell & Nishiura 2014). One way to describe it is as

𝑅𝑜 = 𝛽𝑐′_𝐷,

where 𝑐′ is the contact rate between individuals and 𝐷 is the infectiousness of the disease (i.e. the inverse of the recovery rate from the disease) (Mishra et al. 2011). This expression only holds for the case when the infected individual is located in an entirely susceptible population and when no interventions strategies are in place (Chowell & Nishiura 2014). For the disease prevalence to increase in a population, 𝑅𝑜 must be greater than one. This parameter is therefore an indication of the ability of intervention strategies to reduce or potentially eliminate the secondary spread of disease within a population.

Force of infection

The force of infection (denoted by 𝜆) characterises the transmission between infected and susceptible individuals. This is expressed as

𝜆 = 𝛽𝑐′_𝑝,

which unifies the contact rate 𝑐′, transmission probability 𝛽 and prevalence of the disease (refers to the proportion of individuals in a population which have a disease at a specified point in time, denoted as 𝑝) in order to quantify the transmission dynamics of a disease (Mishra et al. 2011).

Compartmental classification of models

Within epidemiology, the propagation of disease within a population is commonly modelled by means of clustering individuals according to mutually exclusive disease states, a typical approach of epidemiological modelling. Once these states are determined, various mathematical modelling approaches are available to use to describe the movement between different disease states. Four of the most commonly used categories are:

 S, individuals who are susceptible to disease infection, but not yet infected;

 E, individuals who are exposed or infected with disease pathogens, but cannot transmit the disease to other individuals yet;

 I, individuals who are infectious and are able to transmit the disease; and

 R, individuals who are not infectious anymore as a result of disease immunity following recovery or death of the individual.

Additional categories are sometimes also incorporated in modelling approaches (e.g. Q, when infected individuals are quarantined or V when individuals are vaccinated), depending on the nature

of the research questions. Within compartmental models, movement to other disease states are modelled according to transmission probabilities, contact rates and patterns. Mathematical modelling approaches (e.g. differential equations), network models and simulation approaches frequently utilise compartmental classification to characterise disease states.