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Help me please. How can i solve that below equation system ?

$dx/dt=a*x-b*v*x$

$dy/dt=a*y+b*v*x-k*y$

$dv/dt=k*L*y-b*v*x-m*v$

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    You will easily find examples of similar problems on stackoverflow, http://stackoverflow.com/questions/tagged/matlab+differential-equations. If you ask your question there, show that you read these examples and the Matlab documentation and post code that shows your understanding. – 2017-01-03
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    Hmm, another user who asks questions, receives answers but cannot be bothered to [accept](http://math.stackexchange.com/help/someone-answers) them. I simply avoid them. – 2017-01-04

2 Answers 2

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Borrowing code from the stackoverflow question https://stackoverflow.com/questions/17013941/implementation-hyperchaotic-lorenz-in-matlab, one could implement this system and its solution as (untested)

function Y=bacteriophage(a,b,k,L,m,T,x0,y0,v0)
  [T,Y]=ode45(system,T,[x0; y0; v0]);
  function out=system(t,state)
    x = state(1); y=state(2), v=state(3)
    out= [
      a∗x-b∗v∗x;
      a∗y+b∗v∗x-k∗y;
      k∗L∗y-b∗v∗x-m∗v
    ];
  end;
end;

a = 0.1121*exp(0.0634); %replication coefficient of bacteria
b = 1*10^(-6); % the transmission coefficient
k = 0.706;     % the lysis rate coefficient
L = 50;        % the burst size
m = 4.8;       % the decay rate of free phage
x0= 1.9*10^4; % initial condition for x(t)
y0= 5.4*10^3; % initial condition for y(t)
v0= 7.4*10^4; % initial condition for v(t)
T = 0:0.001:3;
Y=bacteriophage(a,b,k,L,m,T,x0,y0,v0)
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Matlab have full support to solve ODE's. You can find the documentation here.

Basically, you will need to create a function defining this system of equations and pass a function handler to ode45 or any other ODE solver. You can find a more detailed explanaition at the links I have indicated.