Question

Consider a Susceptible-Infected-Recovered (SIR)-model. Briefly explain the terms the ‘Basic Reproduction Number’, R0, and the ‘Effective Reproduction Number, R(t). What useful information do they provide about the pandemic? Consider an economy under a pandemic where there remains a very large susceptible population, S. Clearly explain how each of the following two scenarios (i) public health measures (e.g. mitigation and suppression strategies) and (ii) a sudden arrival of an effective vaccine or an effective anti-viral medication is likely to affect R(t). In light of your response, briefly comment on the particular ongoing challenge in affecting the value of R(t) in Canada.

Answer 1

Challenge in affecting the value of R(t)

Susceptible-Infectious-Recovered (SIR) model:

• SIR model is a model which subdivide the populations into compartments such as “Susceptible,” “Infectious,” or “Recovered”. Sometimes the other compartments such as “Exposed but not yet Infectious", Asymptomatic.
• Estimation of those compartments on the sizes that can inform data on cases, hospitalizations or deaths and the equations that is used to describe the speed at which people move from one compartment to the next.   
• Typical mathematical model of infectious disease, that often simplify the virus-host interaction and the evolution of an epidemic into a few basic disease which is stated.
• One of the simplest epidemic model is Susceptible-Infected-Recovered (SIR) model.
• The most popular types of model (SIR) which assigned to everyone in a population in which one of the several categories relying on parameters such as the Contact rate, the Probability of transmission, and the Duration on which someone is infectious.
• Comparing to all the models, “agent-based” models are innovative, that simulates the movement of individuals.
• For both agent-based and SIR models, R0 and Re can be derived from the models themselves.
• Once calculated, these metrics can also play a key role within the models to create predictions about the spread of a disease.
• It is unlikely that the R0 has been calculated in China will be same in the US explains that how many people are infected as individual infects, can also change within localities as governments close essential businesses and issue shelter-in-place orders or to reopen their economy.
• The reproductive number R describes the average number of individuals that a person infected with a particular pathogen infects. It depends on how that pathogen is transmitted as well as how often people come into contact with each other.
• R₀ is affected by the proportion of susceptible people and the density of the population;
• The infectiousness of the organism also the rate of disappearance of cases by recovery or death, the first of which depends on the time for individual who is infective.
• (1) Public Health Measure : Vaccination against a viral infection is the administration of a vaccine to an individual with the intention of immunizing that individual or boosting pre-existing immunity.

Epidemiologists typically distinguish between two forms of the reproductive number R and the basic reproductive number R0 describes the initial spread of an infection in a completely susceptible population, and the effective reproductive number.

Re captures transmission once a virus becomes more common and as public health measures are initiated. Re is typically much lower than R0.

• (2) Immunity to Anti-viral medication is the state of being non-susceptible to produce neutralizing antibodies prior to exposure or by immunization following vaccination.
• ONGOING CHALLENGES: The zero in “R zero” means,it is estimated when there is zero immunity in the population.Not everyone will necessarily be susceptible to infection as usual assumption.
• In an epidemic with a completely new virus, the earlier measurements are made to calculate the value which is likely to the true value of R₀, by assuming the high-quality data. It is better to talk about the transmissibility of the virus by using a different symbol, R_e, the effective reproduction number.
• R₀ predicts the extent of immunization that a population if it requires herd immunity is to be achieved by the spread of infection limited and the population protected against future infection.