neural disease transmission models for inference

Let’s start with an elementary, but yet insightful equation system commonly known as the SIS disease transmission model. Full stop. Let’s start from somewhere else. The fact that biological entitities such as viruses, bacteria and fungi have durably colonized the human body sets the stage for a life-long antagonistic relationship between them and us - the parasites and the hosts. But not only their unfriendly relationship sets them apart from each other, these best enemies live on distinct spatial and temporal scales. Viruses are sized in the micrometers and can only be observed via electronic microscopy, and one virus can produce offspring in the ten thousands within hours or days. On the other hand, multicellular tissue heaps known as humans are sized in meters, and it takes decades for them to reproduce, if at all. The action starts when parasites enter human cells, mainly by tricking their surface proteins and making it into the cellular reproduction machinery. Parasites exploit the host cell for their own metabolism or reproduction. Eventually the host cell will burst like a star allowing the parasite offspring to find its next victim in the cellular environment. But one host is not enough. Insatiable as they are, the parasites need to be transmitted to keep on living, as their fate is bound to the fate of the host.

virus virion

susceptible, infectious infection, contagion, transmission

For a constant total population \(N=S+I\), we consider \(\begin{aligned} \frac{dS}{dt} &= -\beta S \tfrac{I}{N} + \gamma I \\ \frac{dI}{dt} &= \beta S \tfrac{I}{N} - \gamma I \end{aligned}\)

This theme supports rendering beautiful math in inline and display modes using MathJax 3 engine. You just need to surround your math expression with $$, like $$ E = mc^2 $$. If you leave it inside a paragraph, it will produce an inline expression, just like \(E = mc^2\).

To use display mode, again surround your expression with $$ and place it as a separate paragraph. Here is an example:

\[\sum_{k=1}^\infty |\langle x, e_k \rangle|^2 \leq \|x\|^2\]

You can also use \begin{equation}...\end{equation} instead of $$ for display mode math. MathJax will automatically number equations:

\begin{equation} \label{eq:cauchy-schwarz} \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \end{equation}

and by adding \label{...} inside the equation environment, we can now refer to the equation using \eqref.

Note that MathJax 3 is a major re-write of MathJax that brought a significant improvement to the loading and rendering speed, which is now on par with KaTeX.