绘制基本再生数随两参数变化的曲线图技术求助

需要复现指定论文中的图表，以下是基本再生数（R₀）的参数值与计算公式：

beta_s = 0.274
alpha_a = 0.4775
alpha_u = 0.695
mu = 0.062
gamma_a = 0.29
q_i = 0.078
1/eta_i = 0.009 → eta_i = 1/0.009 ≈ 111.111
1/eta_u = 0.05 → eta_u = 1/0.05 = 20

R₀ = (beta_s*alpha_a)/(gamma_a+mu) + (beta_s*alpha_u*gamma_a*(1-q_i))/((gamma_a+mu)(eta_u+mu))

R语言实现代码 #

# 设定基础参数
alpha_a <- 0.4775
alpha_u <- 0.695
mu <- 0.062
gamma_a <- 0.29
q_i <- 0.078
eta_i <- 1/0.009
eta_u <- 1/0.05

# 定义R₀计算函数
calculate_R0 <- function(beta_s) {
  term1 <- (beta_s * alpha_a) / (gamma_a + mu)
  term2 <- (beta_s * alpha_u * gamma_a * (1 - q_i)) / ((gamma_a + mu) * (eta_u + mu))
  return(term1 + term2)
}

# 生成beta_s序列（匹配图表横轴范围）
beta_s_seq <- seq(0, 0.5, by = 0.01)
R0_vals <- sapply(beta_s_seq, calculate_R0)

# 绘制图表
plot(beta_s_seq, R0_vals, type = "l", lwd = 2, col = "blue",
     xlab = expression(beta[s]), ylab = expression(R[0]),
     main = expression("Basic Reproductive Number " * R[0] * " vs " * beta[s]))
abline(h = 1, lty = 2, col = "red") # 添加R₀=1的关键参考线

MATLAB实现代码 #

% 设定基础参数
alpha_a = 0.4775;
alpha_u = 0.695;
mu = 0.062;
gamma_a = 0.29;
q_i = 0.078;
eta_i = 1/0.009;
eta_u = 1/0.05;

% 定义R₀计算匿名函数
calculate_R0 = @(beta_s) ...
    (beta_s * alpha_a)/(gamma_a + mu) + ...
    (beta_s * alpha_u * gamma_a * (1 - q_i))/((gamma_a + mu)*(eta_u + mu));

% 生成beta_s序列（匹配图表横轴范围）
beta_s_seq = 0:0.01:0.5;
R0_vals = arrayfun(calculate_R0, beta_s_seq);

% 绘制图表
plot(beta_s_seq, R0_vals, 'LineWidth', 2, 'Color', 'blue');
xlabel('\beta_s');
ylabel('R_0');
title('Basic Reproductive Number R_0 vs \beta_s');
hold on;
plot([min(beta_s_seq) max(beta_s_seq)], [1 1], '--r', 'LineWidth', 1); % 添加R₀=1的关键参考线
hold off;
grid on;

内容的提问来源于stack exchange，提问作者Hew123