Mathematically modeling spillovers of an emerging infectious zoonosis with an intermediate host

Abstract

Modeling the behavior of zoonotic pandemic threats is a key component of their control. Many emerging zoonoses, such as SARS, Nipah, and Hendra, mutated from their wild type while circulating in an intermediate host population, usually a domestic species, to become more transmissible among humans, and this transmission route will only become more likely as agriculture and trade intensifies around the world. Passage through an intermediate host enables many otherwise rare diseases to become better adapted to humans, and so understanding this process with accurate mathematical models is necessary to prevent epidemics of emerging zoonoses, guide policy interventions in public health, and predict the behavior of an epidemic. In this paper, we account for a zoonotic disease mutating in an intermediate host by introducing a new mathematical model for disease transmission among three species. We present a model of these disease dynamics, including the equilibria of the system and the basic reproductive number of the pathogen, finding that in the presence of biologically realistic interspecies transmission parameters, a zoonotic disease with the capacity to mutate in an intermediate host population can establish itself in humans even if its R0 in humans is less than 1. This result and model can be used to predict the behavior of any zoonosis with an intermediate host and assist efforts to protect public health.

Fig 1. A representation of the model.

Model parameters are summarized in Table 3.

Fig 2. A simulation of low-pathogenic avian influenza mutating to high-pathogenic avian influenza.

Parameters are as shown in Table 5. While the epidemic dies out in the animal species, its R₀ is 2.0871, allowing an epidemic to persist in humans.

Fig 3. β_h (right) and β_d (left) are directly proportional to the proportion of humans infected with the mutated strain.

Fig 4. Graphing the equilibrium proportion of infected humans (I_h) against p_h and p_d for four different values of μ, with β_h = 0.078.

Parameters are as in Table 5, with β_w = β_d = 0.118*5. While intracompartmental reproductive numbers vary between simulations, R₀ for all four simulations is 2.2463.

Fig 5. Graphing the equilibrium proportion of infected humans (I_h) against p_h and p_d for four different values of μ, with β_h = 0.

Parameters are as in Table 5, with β_w = β_d = 0.118*5. While intracompartmental reproductive numbers vary between simulations, R₀ for all four simulations is 2.2463.