How to find fixed points or find the stationary points (numerically) in this system with Matlab?

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I hope help me in this problem. I like find the fixes point in this system.

enter image description here

I wrote a code in Matlab as follow:

clear all;
close all;
clc;
%
tic;
rand('state',sum(100*clock)); % seed
%

numreps=2; % Number of iterations
for j=1:numreps
  options = odeset('RelTol',1e-6,'Stats','on');  
% Parameters values of adults and tadpoles

    % Fecundity (number of new individuals)
    aH = 800; % minimum number offsprings 
              % per each host adults per year
              % Mitchell 2008

    % Metamorphosis rate
    ah = 0.16; % Metamorphosis rate per year
               % Mitchell 2008

    % Natural dead hosts whitout infection 
    bH =  0.73; % Natural mortality rate in adults 
                % per year Mitchell 2008

    bh = 7.55; % Natural mortality rate in adults 
               % per year Mitchell 2008

    % Host mortality due to infection 
    alphaH = 0.001; % Mortality rate per adult host 
                    % per unit time due to infection 
                    % this work

    alphah = 3.25;  % Mortality rate per adult host 
                    % per unit time due to infection 
                    % this work

    % Natural mortality zoospores within hosts
    muH = 117*52; % Natural mortality in zoospores 
                  % in adults Woodhams 2008 at an 
                  % average temperature 17.38 per year

    muh = 117*52; % Natural mortality in zoospores 
                  % in adults Woodhams 2008 at an 
                  % average temperature 17.38 per year

    %zoospore release rate
    lambdaH = 1*10^5; % Release rate of new zoospores 
                        % within the body of the tadpole 
                        % host to the pool per year Mitchel 2008

    lambdah = 6.6*10^5; % Release rate of new zoospores 
                        % within the body of the tadpole 
                        % host to the pool per year Mitchel 2008

    % Zoospores recruitment rate within host
    rH = 124*52; % Maximum birth rate of new zoospores
                 % within the pre-adult host body 
                 % per unit time Woodhams et al 2008

    rh = 124*52; % Maximum birth rate of new zoospores
                 % within the pre-adult host body 
                 % per unit time Woodhams et al 2008

    % Zoospores transmission rate since pool 
    % Mitchell 2008
    betaH = 6*10^-9; % Rate of transmission of a spore
                     % to an individual per year
                     % Mitchell pre-adult 2008 

    betah = 6*10^-9; % Rate of transmission of a spore
                     % to an individual per year
                     % Mitchell pre-adult 2008 

   % Recapture factor of spores that are released by 
    % sporangium from the skin of the hosts
    varrhoH1 = 10^-2;
    varrhoH = varrhoH1*lambdaH; % Proportion of zoospores 
                                % that are immediately absorbed into 
                                % the skin of adult hopederos, 
                                % who depend on the zoospores released 
                                % by sporangiumos sporangios
    varrhoh1 = 10^-2;                                       
    varrhoh = varrhoh1*lambdah; % Proportion of zoospores 
                                % that are immediately absorbed into 
                                % the skin of adult hopederos, 
                                % who depend on the zoospores released 
                                % by sporangiumos sporangios

   % Maximum absorption factor of 
   % zoospores by host values taken 
   % from Woodhams 2008
     phiH = 10^4;  % Inverse absorption factor 
                   % per host, if low 
                   % absorption is high and viceversa

     phih = 10^4;  % Inverse absorption factor 
                   % per host, if low 
                   % absorption is high and viceversa

    % Natural mortality of zoospores into the pool 
    muZ = 45*52; % Tasa de mortalidad natural 
                % de la zoosporas Castro 2015 
                % por año

    % Carrying capacity of species
    KH = 10^5; % adults host
    Kh = 10^5; % tadpoles host


    %x(1) = H; x(2) = h; x(3) = ZH; 
    %x(4) = Zh; x(5) = Z;

    G = @(t, x, ah, aH, bh, bH, muh, muH, alphah, ...
        alphaH, lambdah, lambdaH, rh, rH, phih, phiH, ...
        varrhoh, varrhoH, muZ, betaH, betah, Kh, KH) ...
        [ah *  x(2) * exp(-Kh * x(2)) - bH * x(1) - alphaH * x(3); ...
        aH * x(1) - (bh + ah * exp(-Kh * x(2))) * x(2) - alphah * x(4); ...
        rH * x(3) * exp(-phiH * x(3)) + lambdaH * x(3) * (x(1)./(varrhoH + x(1))) + x(5) * betaH * (x(1)./(x(1) + x(2))) - x(3) * (bH + muH) - alphaH * x(1) * (x(3)./x(1) + (x(3)./x(1))^2 * ((phiH + 1)./phiH)); ...
        rh * x(4) * exp(-phih * x(4)) + lambdah * x(4) * (x(2)./(varrhoh + x(2))) + x(5) * betah * (x(2)./(x(1) + x(2))) - x(4) * (bh + ah * exp(-Kh * x(2)) + muh) - alphah * x(2) * (x(4)./x(2) + (x(4)./x(2))^2 * ((phih + 1)./phih)); ...
        lambdaH * x(3) + lambdah * x(4) - x(5) * (muZ + betaH * (x(1)./(x(1) + x(2))) + betah * (x(2)./(x(1) + x(2))))-(lambdaH * x(3) * (x(1)./(varrhoH + x(1))) + lambdah * x(4) * (x(2)./(varrhoh + x(2))))];
    %tspan = [0:0.001:50];
    x0 = [100 100 10 10 500];
    [t,xa] = ode45(@(t,x) G(t, x, ah, aH, bh, bH, muh, muH, ...
        alphah, alphaH, lambdah, lambdaH, rh, rH, phih, phiH, ...
        varrhoh, varrhoH, muZ, betaH, betah, Kh, KH), ...
        [0 50], x0, options);

    H = xa(:,1)';
    h = xa(:,2)';
    Zh = xa(:,3)';
    ZH = xa(:,4)';
    Z = xa(:,5)';
    end 

The solutions of system above when I make the graphic with this code:

%
figure1 = figure;

% Create axes
axes1 = axes('Parent',figure1);
hold(axes1,'on');

% Create multiple lines using matrix input to plot
plot1 = plot(t,xa,'LineWidth',3,'Parent',axes1);
set(plot1(1),'DisplayName','Adults host, H(t)');
set(plot1(2),'DisplayName','Tadpoles host, h(t)');
set(plot1(3),'DisplayName','Spores into the adults, ZH(t)','LineStyle','--');
set(plot1(4),'DisplayName','Spores into the tadpole, Zh(t)','LineStyle',':');
set(plot1(5),'DisplayName','External Pool of spores, Z(t)',...
'LineStyle','-.');

% Uncomment the following line to preserve the X-limits of the axes
% xlim(axes1,[0 5]);
% Uncomment the following line to preserve the Y-limits of the axes
% ylim(axes1,[-500 3000]);
box(axes1,'on');
grid(axes1,'on');
% Create xlabel
xlabel('Time in years');
% Create ylabel
ylabel('Population size');
% Set the remaining axes properties
set(axes1,'FontSize',12);
% Create legend
legend1 = legend(axes1,'show');
set(legend1,'FontSize',10);
%}

and this is the graphic

ODE solution

according to the previous graph, the solutions of the system converge to fixed points. Is there any way that the fixed points of the previous system can be calculated numerically using Matlab?

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