MATLAB Simulation of Winter Influenza Spread

Recently, the flu has been quite severe. Today, I will create a simulation program for flu transmission based on my city, which requires: susceptible individuals, infected individuals, and recovered individuals. Of course, everyone should pay attention to their health and take precautions!

clear; clc; close all;

%% Parameter Settings

N = 2.7e6; % Resident population

I0 = 10; % Initial infected individuals

R0 = 0;

S0 = N – I0 – R0;

gamma = 1/5; % Recovery rate (5-day illness duration)

beta_base = 0.3; % Base transmission rate (non-winter)

beta_winter = 0.6; % Winter transmission rate

tspan = 0:1:90; % Simulate for 90 days

t_start = datetime(2024,11,1); % Start date

% Input: scalar or vector t (days)

% Output: logical array, true indicates that the day is winter (November–February)

isWinterDayVec = @(t) arrayfun(@(day) …

ismember(month(t_start + days(day)), [11,12,1,2]), t);

% Time-varying beta function

beta_func = @(t) beta_winter .* isWinterDayVec(t) + beta_base .* (~isWinterDayVec(t));

%% SIR Differential Equations (with time-varying beta)

sir_ode = @(t, y) [

-beta_func(t) * y(1) * y(2) / N;

beta_func(t) * y(1) * y(2) / N – gamma * y(2);

gamma * y(2)

];

%% Solve ODE

y0 = [S0; I0; R0];

[~, Y] = ode45(sir_ode, tspan, y0);

S = Y(:,1); I = Y(:,2); R = Y(:,3);

figure(‘Position’,[100,100,900,600]);

subplot(2,1,1);

plot(tspan, S, ‘b-‘, ‘LineWidth’, 1.5); hold on;

plot(tspan, I, ‘r-‘, ‘LineWidth’, 1.5);

plot(tspan, R, ‘g-‘, ‘LineWidth’, 1.5);

xlabel(‘Time (days)’); ylabel(‘Number of individuals’);

title(‘SIR Model Simulation of Winter Influenza in Baotou (Starting November 2024)’);

legend(‘Susceptible S’,’Infected I’,’Recovered R’,’Location’,’best’);

grid on;

[Imax, idx_max] = max(I);

text(tspan(idx_max), Imax, sprintf(‘ Peak: %.0f individuals
Day %d’, Imax, tspan(idx_max)), …

‘VerticalAlignment’,’bottom’,’FontSize’,10,’Color’,’red’);

% Daily new infections ≈ -dS/dt

dS = -diff(S);

t_new = tspan(1:end-1);

subplot(2,1,2);

bar(t_new, dS, ‘FaceColor’,[0.8 0.2 0.2]);

xlabel(‘Time (days)’); ylabel(‘Daily new infections’);

title(‘Estimated Daily New Influenza Cases’);

grid on;

xticks(0:10:90);

date_labels = string(t_start + days(0:10:90));

xticklabels(date_labels);

sgtitle(‘Simulation of Winter Influenza Spread in Baotou (SIR + Seasonal Transmission Rate)’);

fprintf(‘=== Simulation Results Summary ===\n’);

fprintf(‘Peak number of infections: %.0f (Day %d)\n’, Imax, tspan(idx_max));

fprintf(‘Total cumulative infections: %.0f (%.2f%%)\n’, R(end), R(end)/N*100);

The results are as follows:

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Note: The above data (including time) is not real and is for learning reference only.