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8.7.3.21. Viruses¶

Viruses are, like heterotrophic bacteria, considered a ‘plankton’ type in darwin. To make a plankton group viruses, set grp_virus to 1 in data.darwin, or set isvirus to 1 for individual types in data.traits. Set the parameter infected(jS,jV) to a value jI to indicate that virus jV infects susceptible host jS to become infected host jI. As a special case, jI can be equal to jS. In this case, there is no explicit infected type, see below.

8.7.3.21.1. With explicit infected type¶

When jI \(\ne\) jS, infected plankton are represented by a separate type, typically with the same traits as the susceptible type except for a lower growth rate. Denoting the carbon biomass of the three ‘plankton’ types as follows: susceptible, \(S\), infected, \(I\), and viruses, \(V\), the tendencies due to interactions with viruses are

\[ \begin{align}\begin{aligned}\frac{d S}{d t} &= \dots -\epsilon r_{\rm inf} Q^{\mathrm{c}}_S\\\frac{d I}{d t} &= \dots +\epsilon r_{\rm inf} (Q^{\mathrm{c}}_S + Q^{\mathrm{c}}_V) - \frac{1}{\tau} I\\\frac{d V}{d t} &= \dots - r_{\rm inf} Q^{\mathrm{c}}_V + \beta\frac{Q^{\mathrm{c}}_V}{Q^{\mathrm{c}}_I} \frac{1}{\tau} I\\\frac{d\op{DOC}}{d t} &= \dots + (1-\epsilon) r_{\rm inf} Q^{\mathrm{c}}_V + f_{\rm DOM}^{\rm burst} \left(1-\beta\frac{Q^{\mathrm{c}}_V}{Q^{\mathrm{c}}_I}\right) \frac{1}{\tau} I\\\frac{d\op{POC}}{d t} &= \dots + (1-f_{\rm DOM}^{\rm burst}) \left(1-\beta\frac{Q^{\mathrm{c}}_V}{Q^{\mathrm{c}}_I}\right) \frac{1}{\tau} I\\\frac{d\op{DON}}{d t} &= \dots + (1-\epsilon) r_{\rm inf} Q^{\mathrm{c}}_V Q^{\mathrm{N}}_V + f_{\rm DOM}^{\rm burst} \left(Q^{\mathrm{N}}_I-\beta\frac{Q^{\mathrm{c}}_V Q^{\mathrm{N}}_V}{Q^{\mathrm{c}}_I}\right) \frac{1}{\tau} I\\\frac{d\op{PON}}{d t} &= \dots + (1-f_{\rm DOM}^{\rm burst}) \left(Q^{\mathrm{N}}_I-\beta\frac{Q^{\mathrm{c}}_V Q^{\mathrm{N}}_V}{Q^{\mathrm{c}}_I}\right) \frac{1}{\tau} I\\& ...\end{aligned}\end{align} \]

where the individual infection rate in ind/m³/s is

\[r_{\rm inf} = \phi_S \frac{S}{Q^{\mathrm{c}}_S} \frac{V}{Q^{\mathrm{c}}_V}\]

With dynamic CDOM, a fraction fracCDOM of the loss to DOM goes to CDOM (with CDOM stoichiometry).

8.7.3.21.2. Without explicit infected type¶

When jI = jS, infection leads to immediate lysis and the tendencies become

\[ \begin{align}\begin{aligned}\frac{d S}{d t} &= \dots -\epsilon r_{\rm inf} Q^{\mathrm{c}}_S\\\frac{d V}{d t} &= \dots + \beta\frac{Q^{\mathrm{c}}_V}{Q^{\mathrm{c}}_S} \epsilon r_{\rm inf} Q^{\mathrm{c}}_S = \dots + \beta\epsilon r_{\rm inf} Q^{\mathrm{c}}_V\\\frac{d\op{DOC}}{d t} &= \dots + f_{\rm DOM}^{\rm burst} \left(1-\beta\frac{Q^{\mathrm{c}}_V}{Q^{\mathrm{c}}_S}\right) \epsilon r_{\rm inf} Q^{\mathrm{c}}_S\\\frac{d\op{POC}}{d t} &= \dots + (1-f_{\rm DOM}^{\rm burst}) \left(1-\beta\frac{Q^{\mathrm{c}}_V}{Q^{\mathrm{c}}_I}\right) \epsilon r_{\rm inf} Q^{\mathrm{c}}_S\\\frac{d\op{DON}}{d t} &= \dots + f_{\rm DOM}^{\rm burst} \left(Q^{\mathrm{N}}_S-\beta\frac{Q^{\mathrm{c}}_V Q^{\mathrm{N}}_V}{Q^{\mathrm{c}}_S}\right) \epsilon r_{\rm inf} Q^{\mathrm{c}}_S\\\frac{d\op{PON}}{d t} &= \dots + (1-f_{\rm DOM}^{\rm burst}) \left(Q^{\mathrm{N}}_S-\beta\frac{Q^{\mathrm{c}}_V Q^{\mathrm{N}}_V}{Q^{\mathrm{c}}_S}\right) \epsilon r_{\rm inf} Q^{\mathrm{c}}_S\\& ...\end{aligned}\end{align} \]

with \(r_{\rm inf}\) form above.

8.7.3.21.3. Resistent plankton types¶

Resistant plankton types are represented as susceptible types with a reduced infection rate, \(\phi_R<\phi_S\). The growth rate is usually also reduced, \(\mu_R<\mu_S\), as a trade-off. A fraction \(\gamma\) of the growth of either type may be transfered to the other to represent mutations:

\[ \begin{align}\begin{aligned}\frac{d S}{d t} &= \dots -\gamma_{S R} \mu_S S + \gamma_{R S} \mu_R R \;,\\\frac{d R}{d t} &= \dots -\gamma_{R S} \mu_R R + \gamma_{S R} \mu_S S \;.\end{aligned}\end{align} \]

8.7.3.21.4. Parameters¶

Table 8.59 Virus Parameters¶
sym	param	trait param	default	units	comments
	isvirus(jV)	grp_virus	0		1: type jV is a virus
	infected(jS,jV)	grp_infected	0		index of type resulting from infection of host jS with virus jV
\(\phi_S\)	v_absorp(jS,jV)	a_v_absorp	2.7×10⁻¹⁹	m³/s/ind	= 0.27 μm³/ind/s = infection rate per number density
\(\epsilon\)	v_abeff(jS,jV)	a_v_abeff	1	unitless	absorption efficiency
\(\tau\)	v_latent(jS,jV)	a_v_latent	86400	s	latency period
\(\beta\)	v_burst(jS,jV)	a_v_burst	20	virons	burst size
\(f_{\rm DOM}^{\rm burst}\)	v_dompomfrac (jS,jV)	a_v_dompomfrac	0.5	unitless	fraction of burst spoils to DOM
\(\gamma_{jk}\)	bioflux(j,k)	a_bioflux	0	unitless	fraction of growth of type j transferred to k

For allometric trait generation, it is assumed that all plankton in the first group are susceptible to all viruses in the second group (usually just one), so the parameters apply to all types in a group.

This is different for growth transfer, bioflux, which is assumed to go by type within the groups: the first plankton in the source group transforms into the first in the target group, etc.

The carbon content of an individual, \(Q^{\mathrm{c}}_j\) = qcarbon(j), is described in Section 8.7.3.14.1. A typical value for a virus is 2.75×10⁻¹⁵ mmol C/viron. Quotas of infected classes (carbon and other) are computed as a sum of those of the corresponding susceptible and virus classes at model initialization.