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: