# Estimate the effective reproduction number with the next generation matrix approach ```r posterior_rt(object, y_data, age_distribution_population, infectious_period) ``` ## Arguments - `object`: An object of class `stanigbm`. See `stan_igbm`. - `y_data`: data.frame; age-specific mortality counts in time. See `data(age_specific_mortality_counts)`. - `age_distribution_population`: data.frame; the age distribution of a given population. See `aggregate_age_distribution`. - `infectious_period`: integer; length of infectious period in days. Must be >=1. ## Returns A data.frame which can be visualised using `plot_posterior_rt`. ## Examples ```r # Age-specific mortality/incidence count time series: data(age_specific_mortality_counts) data(age_specific_cusum_infection_counts) # Import the age distribution for Greece in 2020: age_distr <- age_distribution(country = "Greece", year = 2020) # Lookup table: lookup_table <- data.frame(Initial = age_distr$AgeGrp, Mapping = c(rep("0-39", 8), rep("40-64", 5), rep("65+" , 3))) # Aggregate the age distribution table: aggr_age <- aggregate_age_distribution(age_distr, lookup_table) # Import the projected contact matrix for Greece: conmat <- contact_matrix(country = "GRC") # Aggregate the contact matrix: aggr_cm <- aggregate_contact_matrix(conmat, lookup_table, aggr_age) # Aggregate the IFR: ifr_mapping <- c(rep("0-39", 8), rep("40-64", 5), rep("65+", 3)) aggr_age_ifr <- aggregate_ifr_react(age_distr, ifr_mapping, age_specific_cusum_infection_counts) # Infection-to-death distribution: ditd <- itd_distribution(ts_length = nrow(age_specific_mortality_counts), gamma_mean = 24.19231, gamma_cv = 0.3987261) # Posterior sampling: rstan::rstan_options(auto_write = TRUE) chains <- 1 options(mc.cores = chains) igbm_fit <- stan_igbm(y_data = age_specific_mortality_counts, contact_matrix = aggr_cm, age_distribution_population = aggr_age, age_specific_ifr = aggr_age_ifr[[3]], itd_distr = ditd, incubation_period = 3, infectious_period = 4, likelihood_variance_type = "linear", ecr_changes = 7, prior_scale_x0 = 1, prior_scale_x1 = 1, prior_scale_contactmatrix = 0.05, pi_perc = 0.1, prior_volatility = normal(location = 0, scale = 1), prior_nb_dispersion = exponential(rate = 1/5), algorithm_inference = "sampling", nBurn = 10, nPost = 30, nThin = 1, chains = chains, adapt_delta = 0.6, max_treedepth = 14, seed = 1) post_rt_summary <- posterior_rt(object = igbm_fit, y_data = age_specific_mortality_counts, age_distribution_population = aggr_age, infectious_period = 4) # Visualise the posterior distribution of the effective reproduction number: plot_posterior_rt(post_rt_summary) ``` ## References Diekmann, O., Heesterbeek, J., and Roberts, M. (2010). The construction of next-generation matrices for compartmental epidemic models. **J. R. Soc. Interface**, 7, 873–-885. Bouranis, L., Demiris, N. Kalogeropoulos, K. and Ntzoufras, I. (2022). Bayesian analysis of diffusion-driven multi-type epidemic models with application to COVID-19. arXiv: [https://arxiv.org/abs/2211.15229](https://arxiv.org/abs/2211.15229)

posterior_rt function