%Model Construction of Bacteria Motility 
 
 %Gaussian distribution of velocity
 v=[1:0.01:20];                %Range of velocities
 v_avg=10;                     %Average velocity v0
 v_dev=v_avg/10;               %Standard Deviation sigma-1
 y1=normpdf(v,v_avg,v_dev);    %Generation of PDF of velocities
 subplot(2,2,1);
 plot(v,y1);
 title('PDF of Bacteria "Run" Velocity')
 xlabel('Velocity'); ylabel('Probability Density'); 
 
 %Gaussian distribution of run-time
 t=[0:0.001:2];                %Range of run duration
 t_avg=1;                      %Average run duration
 t_dev=t_avg/10;               %Standard Deviation sigma-2
 y2=normpdf(t,t_avg,t_dev);    %Generation of PDF of run duration
 subplot(2,2,2); plot(t,y2);
 title('PDF of Bacteria "Run" Duration')
 xlabel('Time'); ylabel('Probability Density');
 
 % Distribution of angles 
 x=[-pi:0.01:pi];              %Range of angle theta
 x_avg=0;                      %Average turn angle
 k=1;                          %Beta factor
 b=besselj(0,k); %Generates a Bessel function of first kind and order 0
 y3=(1/(2*pi*b))*exp(k*cos(x-x_avg)); %Generates the Von Mises distribution
 subplot(2,2,3);
 plot(x,y3);
 Title('PDF of Tumbling Angle');
 xlabel('Tumbling Angle'); ylabel('Probability Density');
 
 % Distribution of tumbling-time
 ts=[0:0.001:0.2];             %Range of tumbling duration
 ts_avg=0.1;                   %Average tumbling duration
 ts_dev=ts_avg/10;             %Standard Deviation sigma-s
 y4=normpdf(ts,ts_avg,ts_dev); %Gernation of PDF of tumbling duration
 subplot(2,2,4); plot(ts,y4);
 title('PDF of Bacteria "Tumbling" Duration')
 xlabel('Time'); ylabel('Probability Density');