Hello, i need help on least square fitting for an infectious disease

An SIR model for COVID-19, Flu, and RSV

We utilize mathematical modeling based on differential equations to investigate the trans-
mission dynamics of the three respiratory infections: COVID-19, Flu, and RSV. To start, let

us consider a simple SIR model, which involves three compartments: the susceptible individ-
uals (denoted by S), the infected individuals (denoted by I), and the recovered individuals

(denoted by R).
The model is described as follows:
dS
dt = Lambda − beta SI − mu S,
dI
dt = beta SI − (gamma + w + mu )I,
dR
dt = gamma I − mu R.

The parameter Lambda is the population influx rate, beta is the transmission rates, mu is the natural
death rate for the human hosts, gamma is the rate of recovery from the infection, and w is the
disease induced death rate. For simplicity, we set Lambda = mu N, where N is the total population.
For the US, mu = 1/76.33 year−1 = 1/(76.33 ∗ 365) day−1

, and N = 345, 426, 571 people.

Other parameter values are:
COVID-19: gamma = 1/14 day−1

, w = 0.01/7 day−1
;

Flu: gamma = 1/3.5 day−1

, w = 0.006/7 day−1
;

RSV: gamma = 1/10.5 day−1

, w = 0.002/7 day−1
.

Apply this model separately to the US data on COVID-19, Flu, and RSV, and estimate the
value of the transmission rate beta in each case. The data fitting is typically done by using the
least squares method. Based on the fitted beta , calculate the basic reproduction number R0
for each.
I am supposed to consider the above instruction to write matlab codes to find the transmission rate for the flu, covid and the RSV data. Each of these diseases has six seasons starting from 2018-2019 seaons to 2023-2024 seasons.
if the matlab data for 2018-2019 flu season is this:
% Filter for the 2018-19 flu season
Flu_data_2018_2019 = Flu_data(strcmp(Flu_data.Season, ‘2018-19’), :);

% Display the filtered data for the 2018-19 season
disp(Flu_data_2018_2019);

% Display the ‘Weekly_Rate’ column (replace with the correct column name if needed)
Weekly_Rate_2018_2019 = Flu_data_2018_2019.WeeklyRate;
disp(Weekly_Rate_2018_2019);
help write a matlab code to find the transmission rate for the 2018-2019 flu season and the reproduction numberAn SIR model for COVID-19, Flu, and RSV

We utilize mathematical modeling based on differential equations to investigate the trans-
mission dynamics of the three respiratory infections: COVID-19, Flu, and RSV. To start, let

us consider a simple SIR model, which involves three compartments: the susceptible individ-
uals (denoted by S), the infected individuals (denoted by I), and the recovered individuals

(denoted by R).
The model is described as follows:
dS
dt = Lambda − beta SI − mu S,
dI
dt = beta SI − (gamma + w + mu )I,
dR
dt = gamma I − mu R.

, and N = 345, 426, 571 people.

Other parameter values are:
COVID-19: gamma = 1/14 day−1

, w = 0.01/7 day−1
;

Flu: gamma = 1/3.5 day−1

, w = 0.006/7 day−1
;

RSV: gamma = 1/10.5 day−1

, w = 0.002/7 day−1
.

% Display the filtered data for the 2018-19 season
disp(Flu_data_2018_2019);

We utilize mathematical modeling based on differential equations to investigate the trans-
mission dynamics of the three respiratory infections: COVID-19, Flu, and RSV. To start, let

us consider a simple SIR model, which involves three compartments: the susceptible individ-
uals (denoted by S), the infected individuals (denoted by I), and the recovered individuals

(denoted by R).
The model is described as follows:
dS
dt = Lambda − beta SI − mu S,
dI
dt = beta SI − (gamma + w + mu )I,
dR
dt = gamma I − mu R.

, and N = 345, 426, 571 people.

Other parameter values are:
COVID-19: gamma = 1/14 day−1

, w = 0.01/7 day−1
;

Flu: gamma = 1/3.5 day−1

, w = 0.006/7 day−1
;

RSV: gamma = 1/10.5 day−1

, w = 0.002/7 day−1
.

% Display the filtered data for the 2018-19 season
disp(Flu_data_2018_2019);

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