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Susceptible-Infected-Recovered-Susceptible Model with Simple Demographics and Vaccination\n\n```r\nSIRS_vaccination_demographics_ode(t, x, params)\n```\n\n## Arguments\n\n- `t`: The timestep over which to calculate derivatives\n- `x`: A numeric vector of compartment populations.\n- `params`: A named vector of parameter values.\n\n## Returns\n\nA vector of derivatives\n\n\n\n## Examples\n\n```r\n##Model Input\nS_u_0 <- 989\nI_u_0 <- 1\nR_u_0 <- 0\nS_v_0 <- 0\nI_v_0 <- 0\nR_v_0 <- 0\nbeta <- 3\ntau <- 2\nchi <- 0.5\nmu <- 1/81\nalpha <- 0.8\nlambda <- 0.7\ndt <- 1\n\nparameters <- c(beta = beta, tau = tau, mu = mu,\n alpha = 0.8, lambda = 0.7)\ninits <- c(S_u = S_u_0, I_u = I_u_0, R_u_0 = R_u_0,\n S_v = S_v_0, I_v = I_v_0, R_v_0 = R_v_0)\n\nSIRS_vaccination_demographics_ode(1, inits, parameters)\n```"}]}]}]}]}]}],["$","div",null,{"className":"lg:w-1/3 lg:border-l px-1 sm:px-8 pt-8 sm:pt-1","children":[["$","div",null,{"className":"mb-8 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