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 $=\backslash$Lambda $\backslash$beta SI $\backslash$mu S$,$

dI

dt $=\backslash$beta SI $(\backslash$gamma $+$ w $+\backslash$mu $)$I$,$

dR

dt $=\backslash$gamma I $\backslash$mu R$.$

The parameter $\backslash$Lambda is the population influx rate, $\backslash$beta is the transmission rates, $\backslash$mu is the natural

death rate for the human hosts, $\backslash$gamma is the rate of recovery from the infection, and w is the

disease induced death rate. For simplicity, we set $\backslash$Lambda $=\backslash$mu N$,$ where N is the total population.

For the US$,\backslash$mu $=1/76\mathrm{.}33$ year$1=1/(76\mathrm{.}33365)$ day$1$

$,$ and N $=345,426,571$ people.

Other parameter values are:

COVID$-19$: $\backslash$gamma $=1/14$ day$1$

$,$ w $=0\mathrm{.}01/7$ day$1$

;

Flu: $\backslash$gamma $=1/3\mathrm{.}5$ day$1$

$,$ w $=0\mathrm{.}006/7$ day$1$

;

RSV: $\backslash$gamma $=1/10\mathrm{.}5$ day$1$

$,$ w $=0\mathrm{.}002/7$ day$1$

$.$

Apply this model separately to the US data on COVID$-19,$ Flu, and RSV$,$ and estimate the

value of the transmission rate $\backslash$beta in each case. The data fitting is typically done by using the

least squares method. Based on the fitted $\backslash$beta $,$ calculate the basic reproduction number R$0$

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, $\text{'}2018-19\text{'}),$ :$)$;

$\%$ 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 number

Please, provide the matlab codes to solve the problem for me