ScenarioTransmission

Levels of Transmission

OpenMalaria simulations of malaria transmission require specification of:

The level and seasonality of exposure (measured by the Entomological Inoculation Rate, EIR) to malaria at the start of the simulation
The model for malaria transmission from humans to mosquitoes
The dynamics of malaria parasite cycle within humans and also the model for transmission from mosquitoes to humans (the entomological model).
The entomological model. There are two different variants of the entomological model:
The "Non-vector" variant does not consider mosquito dynamics and hence does not allow the user to modify the vectorial capacity. It is appropriate for modeling situations where interventions (such as chemotherapy or vaccines that only act on humans) and is described in: Smith et al, 2006.. Specification of this variant is described below
The "Vector" variant comprises discrete-time population models that simulate how many mosquitoes belong in each of several categories at each time. The models assume that the infectious (sporozoite positive) mosquitoes act to distribute infections at random to the human population (with human exposure proportionate to availability). Entomological interventions modify the vectorial capacity and require the "vector" transmission model variant. The simulations that include non-periodic changes in the vectorial capacity use a seasonally forced version of the difference equation model for vector dynamics of Chitnis et al (2008)Journal of Biological Dynamics Vol. 2, No. 3, July 2008, 259–285, further described in Chitnis et al (2010) American Journal of Tropical Medicine and Hygiene Vol. 83, No. 2, 230--240.

The vector transmission model is required for modeling interventions that have effects on mosquitoes, and hence change the vectorial capacity. In addition to the specification described below additional XML parameters for specifying this sub-model are described here.

The default use of both the "non-Vector" and "Vector" model variants follows the original Ross-Macdonald model in assuming that intervention-induced reductions in adult mosquitoes do not affect the numbers of emerging females, (which depend on local carrying-capacity of the breeding sites). OpenMalaria also supports an extension of the "Vector" model variant that incorporates a full-life cycle model that can capture effects of adulticiding on emergence, described here.

Initial level and seasonality of transmission in the nonVector model variant###

The "non vector" model assumes a fixed seasonal vectorial capacity, and either forces infection rates (EIR) or makes EIR dependent on human infectiousness to vectors while forcing vectorial capacity. Initial exposure of humans to infectious mosquito bites is input and any intervention effects on transmission to the mosquito translate into proportionate effects on transmission back to the human. This model is valid when the only interventions are ones that do not affect the vectorial capacity (e.g. vaccines or chemotherapeutic interventions). When vector control interventions are applied, the "Vector" model must be used.

The nonVector element primarily consists of a list of daily EIR (Entomological Inoculation Rate) parameters (EIRDaily elements) specifying the annual EIR (thus 365 values are expected) (see example above). Assuming the first value is the EIR for January 1st, time 0 corresponds to the beginning of the year (since this is the only input affecting seasonality it can be rotated as desired).

Values in this list are averaged per timestep to calculate the EIR per timestep of the year for the pre-intervention equilibrium state. Where data for more than one year are provided, the data is assumed to wrap into the next year and all values for the same timestep of the year are averaged.

nonVector also has an eipDuration attribute: the extrinsic incubation period (sporozoite development time, in days), which determines the delay before changes in human infectiousness affect the EIR (in dynamic mode only).

Entomological data are described by the entomology element, containing either a vector or a nonVector sub-element. For example:

<entomology mode="4" name="a name">
  <nonVector eipDuration="10">
    <EIRDaily origin="monthly">0.0738</EIRDaily>
    <EIRDaily origin="monthly">0.0738</EIRDaily>
    <EIRDaily origin="monthly">0.0738</EIRDaily>
    <EIRDaily origin="monthly">0.0738</EIRDaily>
    <EIRDaily origin="monthly">0.0738</EIRDaily>
    <EIRDaily origin="monthly">0.0738</EIRDaily>
    ...
  </nonVector>
</entomology>

Attributes of the entomology element:

name	versions	type	description
name	versions	type	description
name	all	text	A user-friendly name for the transmission settings

Note that prior to schema 24, the vector model used EIR in units of infectious bites per person per time-period, averaged across the population, while the non-vector model used units of infectious bites per adult per time-period. From schema version 24 both use units of infectious bites per adult per day/timestep/month/year. (The difference being that children receive fewer bites than adults.)

Change EIR

The changeEIR intervention is used to override the default transmission settings. It can only be used with the non-vector transmission model. It is used to simulate the impact of an intervention package with known impact on EIR, either on public health outcomes, or on as a factor modifying the impacts of interventions that can be simulated with the non-vector transmission model. It can be used, for example, to switch to EIR settings recorded during a trial, while retaining the main transmission description for the warm-up and pre-trial periods of the simulation. This intervention updates the transmission model with an entirely new description. It is described like:

<interventions>
  <changeEIR name="name of new transmission settings">
    <timedDeployment eipDuration="10" time="0">
        <EIRDaily origin="interpolate">0.00219</EIRDaily>
        <EIRDaily origin="interpolate">0.00210</EIRDaily>
        <EIRDaily origin="interpolate">0.00202</EIRDaily>
        ...
      </timedDeployment>
  </changeEIR>
  ...
</interventions>

The new EIR is always matched to the whole intervention period, thus must contain enough entries to cover from the beginning of the intervention period to the end, even if not deployed at time 0 or replaced before the end of the simulation. Values are, however, only used from the time of deployment (with some values potentially going unused).

Any number of timedDeployment elements may be used, each of which specifies a time of deployment (in timesteps) and has the same type of content as the nonVector element used to describe the initial transmission.

Deploying a changeEIR intervention changes the transmission mode parameter to static (human infectiousness to mosquitoes has no further effect on EIR).

Entomological Inoculation Rate (EIR) in the vector model variant

In the vector model variant the level and seasonality of transmission are input via a description of the approximate seasonal pattern of the EIR. EIR can be specified either via 5 Fourier coefficients and a rotation factor (EIR element) or via 12 monthly values plus an annual level (monthlyEIR element). Exactly one of these elements must appear. The models require as input, data on the overall average transmission level in the absence of interventions (measured by the entomological inoculation rate, EIR).

Data on seasonality of malaria transmission for driving models might be available in the form of seasonality in any of a number of malariological indices (see Table below). The models, however, expect the seasonality in the EIR as the input. If the data are available in the form of a different measure of seasonality, they need to be transformed before being used to drive the models. The easiest approximation is to introduce a fixed lag period, depending on which measure is used. While this is a considerable simplification, because it assumes proportionality between different measures, this may be reasonable, especially if the data relate to mosquito densities or emergence rates.

The table contains suggestions for what might be the approximate lag periods between different measures of seasonality. A positive value (Lx) for the lag for measure x implies that the EIR seasonality reflects the value of x, Lx days previously. This table provides only a very approximate guide with values rounded to multiples of 5 days. The actual average lag periods in the simulations are model dependent and will vary somewhat from these. The lag periods in the field also vary and, in the case of quantities measured in the vector population, are dependent on the environmental temperature.

Table: Approximate lag periods between different seasonality measures

Transmission measure	Lag period (Lx) (days)
Rainfall	+30
Emergence rate of vector	+20
Density of host-seeking vectors	+10
Entomological inoculation rate	0
Incidence of infection	-5
Incidence of patent infection	-10
Incidence of clinical malaria	-15
Incidence of severe malaria	-20

Ways of specifying level and seasonality in EIR

EIR can be specified either via 5 Fourier coefficients and a rotation factor (EIR element) or via 12 monthly values plus an annual level (monthlyEIR element). Exactly one of these elements must appear.

EIR via Fourier coefficients

This is the older method (the only available method before schema version 22).

The EIR element describes the Entomological Infection Rate for this mosquito species, which is used as a target when fitting the emergence rate of adult mosquitoes. The EIR is given via a Fourier series and a rotation offset; more accurately, the exposed EIR, in units of bites per day, is:

img/eqns/EIR_Fourier.png

<a href='Hidden comment: Above image rendered as latex from: \Xi_t = \exp \left( a_0 + \sum_{n=1}^2 \left[ a_n \cos \left(n (w t - \theta) \right) + b_n \sin \left(n (w t - \theta) \right) \right] \right) (Use, for example, [http://sciencesoft.at/latex/?lang=en] with the AMS maths formula template.)

MathML version (not so nice and less compatible): <wiki:gadget url="http://mathml-gadget.googlecode.com/svn/trunk/mathml-gadget.xml" border="0" up_content="eir_t = exp ( a_0 + sum_(n=1)^2 { a_n cos(n (w t - theta)) + b_n sin(n (w t - theta)) } )"/>

(Formula uses MathML. For IE, a [http://www.dessci.com/en/products/mathplayer/ plugin] is needed.)'>

Here, Ξ_t is the number of innoculations per person per day, where t is the day of year (from 0 to 364), w = 2π / 365, θ is the EIRRotateAngle attribute and a₀ to a₂, b₁ and b₂ are the corresponding attributes of the EIR element.

If we introduce the function f(t) dependent on a_n and b_n for n≥1, we can reformulate Ξ_t as

img/eqns/EIR_Fourier_f.png

and thus show that the annual EIR is scaled by img/eqns/exp_a0.png :

img/eqns/EIR_Fourier_annual.png

This is configured using a section in the XML, per species, similar to the following:

<seasonality annualEIR="178.60558666831946" input="EIR">
          <fourierSeries EIRRotateAngle="0">
            <coeffic a="-0.692164" b="0.002098"/>
            <coeffic a="0.401189" b="-0.375356"/>
          </fourierSeries>
        </seasonality>

EIR via monthly values

As of schema version 22 this method of entering EIR was added to simplify entry of field data. Fourier coefficients are still used within the code (for smoothing), but are calculated internally.

The monthlyEIR element requires one attribute: annualEIR, specifying the total annual EIR as infectious bites per person per year. It should have a sequence of 12 child elements, named item, specifying the relative in terms of infectious bites per person per month (which might be approximated by densities of mosquito densities, with an appropriate lag), in the months of January through December. The overall EIR is scaled to the annualEIR value indicated at the top of the element. An (unrealistic) example:

        <seasonality annualEIR="20" input="EIR">
          <monthlyValues smoothing="fourier">
            <value>10</value>
            <value>1</value>
            <value>1</value>
            <value>1</value>
            <value>1</value>
            <value>1</value>
            <value>1</value>
            <value>1</value>
            <value>1</value>
            <value>1</value>
            <value>1</value>
            <value>1</value>
          </monthlyValues>
        </seasonality>

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