Epidemiology of Streptolossus Particular (SP) Transmission in Country C1 and Vaccine Strategies

Streptolossus particular (SP) is a novel bacterial strain that causes a highly severe disease in adults. (Note that this bacteria is entirely fictional). It results in immunity that we know lasts at least 2 years. In children, infection leads to asymptomatic infection. A vaccine is available for SP (vaccine alpha) which prevents infection. As this is a new bacterial strain, there are limited doses of vaccine alpha. SP is present in country C2 but has yet to be detected in country C1. The Department for Health in country C1 wants to explore how best to utilise the first available, limited doses of vaccine alpha if an outbreak of SP occurs there.
The public health authorities in country C1 have commissioned you and another team to investigate potential vaccine strategies. A decision must be made on how best to implement the vaccine with the limited number of doses of vaccine alpha available. The main public health concern is to limit the number of cases, but also to understand the impact on immunity, as subsequent waves of infection are expected. The other modelling team (from Definite Data Analytics, “DDA”) has already provided some analyses and modelling but are inexperienced in modelling disease dynamics.
Your assignment is to carry out your own modelling work, critically appraise the research of the other modelling team and make recommendations based on the model results from both teams (if appropriate).
Country C2 commissioned a study (Study P) to determine the seroprevalence of SP. At the time of the study, no vaccines were available to prevent this disease and little data were available on the prevalence of SP. There is only one serotype of SP. Study P was a cross-sectional study carried out across country C2. Blood samples were taken from individuals and analysed for the presence of IgG (an antibody that indicates exposure to infection) against the only serotype of SP. Age-specific serology from Study P are available for analysis, in addition to other data on population prevalence. The population structures of Countries C1 and C2 are highly similar. 

We would like you to prepare a report that assesses the epidemiology of SP transmission in country
C1 and the impact of different vaccine strategies. There should be four sections:
1) Analysis of the serological survey
? Estimation of the age-specific force of infection and R0 from the Study P serological data
? Suggested tool: Excel
2) Your mathematical modelling
? Dynamics of infection and disease
? Impact of limited vaccine doses
? Suggested tool: Berkeley Madonna
3) A critical analysis of the DDA model
? Provide some feedback on the report and analysis presented and compare to your own results

Part 1: Estimation of transmission parameters from serological data
To estimate the force of infection from serological data, we suggest using the “Solver” function in MS Excel (see technical section for support if needed).
The age-specific force of infection estimates can then be used to estimate a suitable WAIFW matrix for Part 2. Ensure that your calculations are in the correct units, typically per year.
Part 2: Mathematical model
AIM: Determine the best of three strategies for use of limited vaccine doses The Department of Health would like to know which of three vaccine strategies to implement given the limited number of doses of vaccine alpha available this year. They can use existing infrastructure to give the vaccines.
They would like to know which of the following is more effective at reducing total case numbers over a two-year period:
(1) Giving all vaccines to children (<= 16)
(2) Giving all vaccines to adults
(3) Allocating half of the vaccines (425,000) for children and half for adults
Recall that, there are only 850,000 adult vaccine doses available, sufficient to vaccinate 850,000 adults or 1,700,000 children. The vaccine efficacy is 80% and protection lasts for at least 2 years. Assume that all vaccine doses are delivered at the start of year 1 and no vaccines are given in year 2. Assume that protection is “all or nothing” i.e. that 80% of those that are given the vaccine at the start of the year are fully protected for 2 years.
Use your model to compare the number of cases in adults over two years, with and without the vaccine, as well as the total number of individuals with immunity (both naturally acquired and from the vaccine) at the end of the two years. You may also wish to report any other indicatorsthat could be useful. Assume that the bacterium is introduced into C1 by 1 infectious child at the start of the first year. In your report you should provide your model equations and the way that you incorporated vaccination. Discuss and interpret your results.