Problem with Finite Difference Scheme

Hello, I'm trying to build the finite difference scheme for this task

I build the finite difference scheme like this

The main problem is boundary conditions for theta, because boundary values on its edges don't depend of other counted values. Here is my code, maybe I made a mistake in it?

clc;
clear all;

%constants
r0=0.1;
a=1.01;
b=1;
mu=1;
c=100;

%step-size for r
n=100;
r_max=1;
hr=r_max/n;
r=0:hr:r_max;
nr=max(size(r));

%step-size for theta
m=200;
th_max=2*pi;
hth=th_max/m;
th=0:hth:th_max;
nth=max(size(th));

%step-size for t
l=100;
t_max=5;
ht=t_max/l;
time=0:ht:t_max;
nt=max(size(time));

u=zeros(nr,nth,nt);
v=zeros(nr,nth,nt);

%Initialization
for i=1:nr
    for j=1:nth
        if ((i*hr<=r0)&&(0<=th(j))&&(th(j)<=pi/6))
           u0=0; 
        elseif ((i*hr<=r0)&&(pi/6<th(j))&&(th(j)<2*pi))
           u0=1;
        elseif ((i*hr>r0)&&(0<=th(j))&&(th(j)<=2*pi))
           u0=0; 
        end
        u(i,j,1)=u0;
    end
end

for i=1:nr
    for j=1:nth
        if ((r(i)<=r0)&&(0<=th(j))&&(th(j)<=pi/6))
           v0=1; 
        elseif ((r(i)<=r0)&&(pi/6<th(j))&&(th(j)<2*pi))
           v0=0;
        elseif ((r(i)>r0)&&(0<=th(j))&&(th(j)<=2*pi))
           v0=0; 
        end
        v(i,j,1)=v0;
    end
end

for t=1:nt-1

      for i=2:nr-1

          for j=2:nth-1
          u(i,j,t+1)=u(i,j,t)+ht*((u(i+1,j,t)-2*u(i,j,t)+u(i-1,j,t))/hr^2+(1/(i*hr)))*((u(i+1,j,t)-u(i,j,t))/hr)+(1/(i*hr)^2)*((u(i,j+1,t)-2*u(i,j,t)+u(i,j-1,t)/hth)+u(i,j,t)*(1-u(i,j,t)-c*v(i,j,t)));
          v(i,j,t+1)=v(i,j,t)+ht*((v(i+1,j,t)-2*v(i,j,t)+v(i-1,j,t))/hr^2+(1/(i*hr)))*((v(i+1,j,t)-v(i,j,t))/hr)+(1/(i*hr)^2)*((v(i,j+1,t)-2*v(i,j,t)+v(i,j-1,t)/hth)+a*v(i,j,t)*(1-c*u(i,j,t)-b*v(i,j,t)));

          %Boundary
          u(1,j,t)=u(2,j,t);
          u(nr,j,t)=u(nr-1,j,t);
          v(2,j,t)=v(1,j,t);
          v(nr,j,t)=v(nr-1,j,t);
          u(i,nth,t)=u(i,1,t);
          v(i,nth,t)=v(i,1,t);
          end

      end
  end