How can I obtain the transfer function from these two transfer functions in this case? Using Scipy signal in Python I want to obtain a transfer function for an input which passes first from sys1 and then sys2. So explicitly
$$\text{input}{\longrightarrow}\boxed{\tt sys1}{\longrightarrow}\boxed{\tt sys2}{\longrightarrow}\text{output}$$
sys1 = signal.lti([a], [b, c])

sys1 = signal.lti([x], [y, z])

How can I cascade sys1 and sys2 programatically to obtain the overall transfer function (call it sys_total) between the input and output?
The numerator and denominator of the total system are respectively the convolution of the numerators and the denominators of the filters to be cascaded.
$$
b(n)=b_1(n)*b_2(n)
$$
$$
a(n)=a_1(n)*a_2(n)
$$
You can validate it by the following code in MATLAB
b = conv(b1, b2);
a = conv(a1, a2);

sys1 = dfilt.df2t(b1, a1);
sys2 = dfilt.df2t(b2, a2);
sys = cascade(sys1, sys2);
[b, a] = tf(sys); % convert system object to coefficients