Describe Vacamole model adapted for {epidemics}

[pratikunterwegs]

This issue is a model description and a discussion location for the addition of the Vacamole model to {epidemics}.

Vacamole is a deterministic, compartmental epidemic model built by Kylie Ainslie and others at RIVM, the Dutch Public Health Institute for the Covid-19 pandemic, with a focus on scenario modelling for hospitalisation and vaccination.

Vacamole was implemented as an R package, but is not actively maintained and cannot be installed from its source code. Some versions have been used to generate scenarios for the ECDC Covid-19 Scenario Hub.

Model code: https://github.com/kylieainslie/vacamole Manuscript describing the model and its application: https://doi.org/10.2807/1560-7917.ES.2022.27.44.2101090

The original model has 8 conceptual compartments - four epidemiological compartments: susceptible, exposed, infectious, and recovered (S, E, I, R respectively), three hospitalisation compartments: hospitalised, in intensive care, and returning from intensive care to regular hospital care (H, ICU, ICU2H), and death - see the manuscript describing them here. Only infected individuals can enter the hospitalisation or death compartments.

Individuals from the susceptible compartment may be vaccinated partially ($V_1$) or fully ($V_2$; assuming a two dose regimen), with each dose reducing their probability of being infected, and of being hospitalised or dying.

Modifications for epidemics

We have made some modifications to the ODE model of Vacamole in order to make it more general and thus potentially more applicable to a wider range of settings.

Specifically,

1. We have dropped the ICU and ICU2H compartment as this is potentially less relevant to a context in which intensive care capacity is low.

2. We have added transitions from the infectious (I) and hospitalised (H) compartments to death (D), as this may be a more general assumption when hospital capacity is low (relatively more I → D) or when treatments are poor (relatively more H → D).

3. We assume, in a first pass implementation that vaccination primarily reduces adverse outcomes, by modification to the transition rates ($\betaV,\eta{V},\omega_V$):

   1. $\beta_V$: The infection rate $\beta$ for individuals in the fully vaccinated compartment $V_2$;

   2. $\eta_{V}$: The hospitalisation rate $\eta$ for fully vaccinated, infected individuals ($I_V$ → $H_V$);

   3. $\omega_V$: The mortality rate for all fully vaccinated individuals at any stage in or post infection (I, or H).

Vacamole ODE system for {epidemics}

The Vacamole ODE system adapted for {epidemics} is:

Susceptibles who are not vaccinated, or only partially vaccinated (considered unprotected) can transition to exposed and vaccinated:

$$dS = -\beta S(I+I_V) - \nu_1 S$$

Two sequential vaccination compartments, with a lower conversion rate from two-dose vaccinated individuals (considered to be protected) to exposed:

$$dV_1 = \nu_1S - \beta V_1(I+I_V) - \nu_2V_1$$

$$dV_2 = \nu_2V_1 - \beta_VV_2(I+I_V)$$

Two parallel exposed compartments, with similar conversion to infectious:

$$dE = \beta (S+V_1)(I+I_V) - \alpha E$$

$$dE_V = \beta_VV_2(I+I_V) - \alpha E_V$$

Two parallel infectious compartments, with lower hospitalisation and mortality rate for vaccinated:

$$dI = \alpha E - \gamma I - \eta I - \omega I$$

$$dI_V = \alpha E_V - \gamma IV - \eta{V} I_V - \omega_V I_V$$

Two parallel hospitalisation compartments, with a lower mortality rate for vaccinated:

$$dH = \eta I - \gamma H - \eta_2 H - \omega H$$

$$dHV = \eta{V} I - \gamma H_V - \omega_V H_V$$

Single recovered compartment:

$$dR = \gamma(I + H + I_V + H_V)$$

Single mortality compartment:

$$dD = \omega(I + H) + \omega_V(I_V + H_V)$$

[pratikunterwegs]

The current model structure is chosen with reference to empirical findings from the Covid-19 pandemic, that vaccinated individuals are less likely to be infected, and less likely to suffer adverse outcomes from infection (hospitalisation and death).

This model structure could be simplified in two different ways:

1. Two-dose vaccination only reduces the rate at which individuals are infected ($\beta$ by a factor), but has no effect on further infection compartment transitions;
2. Two-dose vaccination reduces all transition rates by a uniform factor;
3. Removing the H, ICU, and D compartments which may not add much information and which could be estimated separately from known conversion rates. The H compartment might become important for outbreaks where hospitalisation also indicates quarantine, as these individuals are no longer available to infect others.

Conversely the model could be made more complex to reflect that:

1. Some vaccinated individuals might never become infectious, and transition directly to the recovered compartment;
2. The mortality rate increases when individuals enter more serious healthcare compartments (e.g. ICU > H > I).

[pratikunterwegs]

Hi @bahadzie I'm just reopening this issue - the idea with the "Discussion" issues is that they remain open even when they're marked as done.

[bahadzie]

Apologies @pratikunterwegs I thought I clicked on the dropdown arrow next to the 'Close with comment' button to see what other options were available.

[pratikunterwegs]

Closing as this model is stable.