.. include:: ../defs.hrst

.. _Viruses:

Viruses
^^^^^^^

To turn plankton type jv into a virus, set :varlink:`isvirus`\ (jv) to 1 and
set :varlink:`v_absorp`\ (js,jv) to the absorption rate for any susceptible
plankton type js.  Set :varlink:`isinfect`\ (js,jv) to the number of the
infected type js turns into when infected by jv.  For other parameters, see
:numref:`tab_phys_pkg_darwin_virus_parameters`.

Dynamic equations
'''''''''''''''''

Denote with :math:`S` the biomass of the susceptible plankton type, with
:math:`I` that of the infected type and with :math:`V` that of the virus type.
Viral dynamics adds the following tendencies to the model equations:

.. math::

   \partial_t S &= -\frac{\epsilon\varphi}{Q_{\mathrm{V}}} S V \\
   \partial_t I &= +\frac{\epsilon\varphi}{Q_{\mathrm{V}}} S V
                   +\frac{\epsilon\varphi}{Q_{\mathrm{S}}} S V -\frac{1}{\eta} I \\
   \partial_t V &= +\beta \frac{Q_{\mathrm{V}}}{Q_{\mathrm{S}}} \frac{1}{\eta} I
                   -\frac{\varphi}{Q_{\mathrm{S}}} S V \\
   \partial_t\op{DOM} &= \alpha (1-\beta \frac{Q_{\mathrm{V}}}{Q_{\mathrm{S}}}) \frac{1}{\eta} I
                          +(1 - \epsilon) \frac{\varphi}{Q_{\mathrm{S}}} S V \\
   \partial_t\op{POM} &= (1-\alpha) (1-\beta \frac{Q_{\mathrm{V}}}{Q_{\mathrm{S}}})
                          \frac{1}{\eta} I \\

:math:`Q_{\mathrm{S}}` is the carbon quota of the susceptible type as used in
allometric trait generation.  The other parameters are listed in
:numref:`tab_phys_pkg_darwin_virus_parameters`.


Runtime parameters
''''''''''''''''''

.. csv-table:: Darwin virus parameters
   :delim: &
   :widths: 7,24,11,58
   :header: , Name, Type, Description
   :name: tab_phys_pkg_darwin_virus_parameters

                          & :varlink:`isvirus`\ (jv)         & INTEGER & 1: plankton type jv is a virus
                          & :varlink:`isinfect`\ (js,jv)     & INTEGER & >0: type jv infects type js to become type isinfect(js,jv)
   :math:`Q_{\mathrm{V}}` & :varlink:`v_quota`\ (jv)         & _RL     & virus carbon quota [mmol C/viron]
   :math:`\varphi`        & :varlink:`v_absorp`\ (js,jv)     & _RL     & specific virus absorption rate [:math:`m^3/s/`\ individual]
   :math:`\epsilon`       & :varlink:`v_abeff`\ (js,jv)      & _RL     & absorption efficiency
   :math:`\eta`           & :varlink:`v_latent`\ (js,jv)     & _RL     & latency period [s]
   :math:`\beta`          & :varlink:`v_burst`\ (js,jv)      & _RL     & burst size [#virons]
   :math:`\alpha`         & :varlink:`v_dompomfrac`\ (js,jv) & _RL     & fraction if burst going to DOM

So far only fixed elemential ratios are supported.