A Bayesian approach to the calculation of the extrinsic
incubation period
Given the Briére equation (Briére et al . 1999) we first use
Bayesian methods to find the best estimates for the parameters
Tmin, Tmax and c (Gelman et al .
2013, Bolstad et al . 2016, McElreath 2016). Bayesian inference
approach allows us to incorporate prior knowledge into a description of
data, capturing parameter uncertainties. It also provides a consistent
framework for including prior information, while accounting for
uncertainty in inferred parameters.
We used thermodynamic models to estimate the influence of both mean and
diurnal temperature fluctuation on malaria transmission (Paaijmanset al . 2009). Specifically, we selected parasite species that
have been recorded in the western Himalayan birds. We extracted the
temperature dependent EIP values for two human malaria parasites -P. falciparum , P. vivax and avian parasites in the genusPlasmodium (Plasmodium relictum ), Haemoproteus andLeucocytozoon using parasite specific temperature data summarised
in Suppl. Table 1. Specifically, for Haemoproteus , we choose the
average (midpoint of the range) as only temperature ranges were
available (Suppl. Table 1).
To estimate the EIP of a parasite species, two main parameters are
required: the lifespan of arthropod vectors and temperature data. The
two human malaria parasites - P. falciparum , P. vivax are
transmitted by species of Anopheles mosquito. The avian malaria,P. relictum, is primarily transmitted by Culex
quinquefasciatus . It takes the malaria parasite 56 days to develop in
the mosquito at 18°C which is longer than the lifespan of the
mosquitoes. At 22°C it takes only 19 days and at 30°C only 8 days
(Githeko 2007). The upper limit of longevity of mosquitoes can be up to
56 days as used in previous studies (Craig et al . 1999,
Paaijmaans et al . 2009) depending upon environmental conditions.
We considered an upper threshold for the EIP for mosquitoes as 56 days.
The vectors of Haemoproteus sp. are biting midges
(Culicoides sp.) and black flies (simulids) forLeucocytozoon . The lifespan of biting midges is
~10 to 20 days (Sick et al . 2019) whereas black
flies can survive for two to three weeks (Adler 2004). We thus
considered the upper threshold for the EIP for both biting midges and
black flies to be 20 days.
We describe our methods in more detail in subsections below: