给定以下系统：

我如何以数字方式求解系统。当我尝试解决这个问题时，我得到了错误。

/home/gideon/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:19：RuntimeWarning：>除以在double_scalars中遇到的零

/home/gideon/anaconda3/lib/python3.7/site-packages/scipy/integrate/odepack.py:247：>ODEintWarning：检测到非法输入（内部错误）。以 full_output = 1 运行以获得>定量信息。警告.warn(warning_msg, ODEintWarning)

这是我的代码

'''
   x[0]  : P(t). population not infected
   x[1]  : I(t). population Infected
   k     : population carrying capacity
   alpha : growth rate
   rho   : death rate
   beta  : infection rate
   t     : time
'''


t = np.linspace(0,20,50)
fig,ax = plt.subplots(1,figsize = (10,4))
plt.suptitle('Infection Model')

def update_plot(k,alpha,rho,beta):
   ax.clear()

   xprime = lambda x,k,alpha,rho,beta,t: np.array([alpha*x[0]*(1-(x[0]/k))-beta*x[0]*x[1],
                                            beta*x[0]*x[1]-rho*x[1]])
   x0 = np.array([(4/5)*k,k/5])
   x = odeint(xprime,x0,t,args=(k,alpha,rho,beta,))
   y1 = x[:,0]
   y2 = x[:,1]
   ax.plot(t,y1,'b',label = 'P(t)')
   ax.plot(t,y2,'g--',label = 'I(t)')
   plt.legend(loc = 'best')
   plt.show()


k = widgets.FloatSlider(min=1,max = 10 , value =1, description = 'K :')
alpha = widgets.FloatSlider(min=1,max = 10 , value =1, description = r'$\alpha$ :')
rho = widgets.FloatSlider(min=1,max = 10 , value =1, description = r'$\rho$ :')
beta = widgets.FloatSlider(min=1,max = 10 , value =1, description = r'$\beta $ :')

widgets.interactive(update_plot,k=k,alpha=alpha,rho=rho,beta=beta)

我正在尝试绘制系统以获取不同的参数，但我得到的图表不正确。我认为这是由于我在解决方案数组中获得的 nan 值$x$