Error using dsolve in system of first order differential equation

Hi I am trying to solve a system of ODEs using matlab but am getting errorrs. Here is my code.

a and b are constants

syms S(t) I(t) R(t) a b

eqns = [diff(S,t)== -a*S*I, diff(I,t)==a*S*I-b*I,diff(R,t)==b*I];

ans = dsolve(eqns)

Warning: Unable to find explicit solution.

> In dsolve (line 201)

then I tried this

ans = dsolve(eqns,'Implicit',true)

and got the following

Error using char

Conversion to char from logical is not possible.

Error in dsolve>mupadDsolve (line 286)

if isvarname(char(args{end}))

Error in dsolve (line 194)

sol = mupadDsolve(args, options);

Answer 1

[Vaibhav]

Hi Arjun

It seems you are facing issues with solving a system of ordinary differential equations (ODEs).

Due to the nature of your system, an explicit solution might not be available. In such cases, numerical methods are typically used. Functions like ode45, ode23, and ode113 are suitable for obtaining numerical solutions.

Here is how we can approach it:

% Define constants
a = 0.1; % Example value
b = 0.05; % Example value

% Initial conditions [S0, I0, R0]
y0 = [0.99, 0.01, 0]; % Example initial conditions

% Time span
tspan = [0 100]; % From time 0 to 100

% Solve the system
[t, y] = ode45(@(t, y) SIRModel(t, y, a, b), tspan, y0);

% Plot the results
plot(t, y)
legend('S', 'I', 'R')
xlabel('Time')
ylabel('Population')
title('SIR Model Solution')


function dydt = SIRModel(t, y, a, b)
    S = y(1);
    I = y(2);
    R = y(3);
    dydt = [-a*S*I; a*S*I - b*I; b*I];
end

Hope it helps!