key: cord-0685897-7n69edfg authors: Royce, Katherine title: Application of a novel mathematical model to identify intermediate hosts of SARS-CoV-2 date: 2021-05-24 journal: J Theor Biol DOI: 10.1016/j.jtbi.2021.110761 sha: 9bd31232e3ba1c85942e4ec1b701abd17cc7afed doc_id: 685897 cord_uid: 7n69edfg Intermediate host species provide a crucial link in the emergence of zoonotic infectious diseases, serving as a population where an emerging pathogen can mutate to become human-transmissible. Identifying such species is thus a key component of predicting and possibly mitigating future epidemics. Despite this importance, intermediate host species have not been investigated in much detail, and have generally only been identified by testing for the presence of pathogens in multiple candidate species. In this paper, we present a mathematical model able to identify likely intermediate host species for emerging zoonoses based on ecological data for the candidates and epidemiological data for the pathogen. Since coronaviruses frequently emerge through intermediate host species and, at the time of writing, pose an urgent pandemic threat, we apply the model to the three emerging coronaviruses of the twenty-first century, accurately predicting palm civets as intermediate hosts for SARS-CoV-1 and dromedary camels as intermediate hosts for MERS. Further, we suggest mink, pangolins, and ferrets as intermediate host species for SARS-CoV-2. With the capacity to evaluate intermediate host likelihood among different species, researchers can focus testing for possible infection sources and interventions more effectively. Zoonotic disease emergence has proven a significant threat to global health, and yet little is known about the process by which novel pathogens emerge. Zoonotic pathogens circulate in and have adapted to an animal species, the reservoir host, and are sometimes transmitted to other animal species to which 5 they are less well-adapted, usually causing more severe illness. Such intermediate host species, generally a domestic or human-adjacent population, provide a meeting ground where evolutionary pressure and higher exposure to humans can cause a pathogen to mutate from one adapted to its reservoir host to a more human-transmissible form (Neumann et al., 2009 [1] ). Coronaviruses, responsi- 2020 [6] ). In addition, SARS-CoV-2 has been shown to replicate in bat intestinal epithelial cells (Zhou et al., 2020 [7] ). However, while bats harbor an impressive 20 diversity of coronaviruses and are a likely reservoir host for all three epidemic coronaviruses (Liu et al., 2020 [6] ), intermediate host species form a key link in the emergence of each human pathogen. Intermediate hosts are a crucial factor in the emergence of all three coronaviruses, which can adapt to different host species with ease due to their high mutation rate, large genome size, and 25 high recombination rates during mixed infections of a single host (Li et al., 2006 [8] ; Bolles et al., 2011 [9] ). SARS-CoV-1 emerged into the human population through palm civets, P. larvata (Cui et al., 2019 [3] ); although research has cast doubt on whether palm civets were a true intermediate host or merely infected by secondary transmission from initial human cases, the civet population formed 30 a key link in the amplification of SARS-CoV-1 in humans and a resource for it to persist outside humans (Bolles et al., 2011 [9] ). On the other hand, MERS required the presence of an intermediate host species, in this case dromedary camels (C. dromedarius), to adapt to humans, since its R 0 in humans is lower than the threshold of 1 needed to cause an epidemic (Reusken et al., 2013 [10] ; [12] ). SARS-CoV-1 also 40 seems to have persisted in palm civets, rather than its true reservoir host, between its spillovers in 2003 and 2004 (Shi and Hu, 2008 [13] We have modified the introductory intermediate host model presented by intrinsic to the intermediate host species. The full list of ten differential equations, grouped into three linked SIR models, is reproduced for convenience in Tables 1 and 2, and a full justification of the system can be found in the original paper (Royce and Fu, 2020 [18] ). This earlier analysis computes the global R 0 100 of the pathogen as the maximum of each species R 0 using a next-generation matrix, and introduces a quantitative tool for analyzing transmission dynamics that include intermediate host species. Firstly, where the original model did not distinguish between disease dy- We define the intermediate host species parameters (Table 3) is scaled by a factor of σ r , simulating a pathogen that spreads less easily in a new species. We assume that once the pathogen evolves to match its new host, it regains its former transmission rate (β im = β r ). We have not modified the recovery rates in the intermediate host species, γ iw and γ im , since a similar 145 scaling would cancel in the calculation of R 0 = β γ and produce an effectively unchanged pathogen strain. While we initially modeled the transmission rate of the pathogen in humans by scaling β im by a factor of σ h , this choice led to SARS and MERS epidemics with values of R 0 higher (4.86 and 1.04) than those seen is calculated from a simple similarity matrix for each potential IH species (see Table 5 ). σ i is calculated by considering biological factors affecting the susceptibility of the species to the pathogen, κ i by considering the ecology of the species in question, and ρ i by evaluating the typical role the species plays in its natural environment or its use by humans. Definition produces lower values for R 0 . Biologically, although this framework gives the transmission rate of the pathogen in humans in terms of the transmission rate 155 of the wild strain rather than the mutant, the added factor may represent the challenges inherent to adapting to multiple new host species in a timespan of months. Parameter Function We assume the transmission rate between species is directly proportional to both the Table 4 175 summarizes the definitions for each modified transmission parameter. To calculate the intermediate host species parameters, we assign a binary score for each of the questions summarized in Table 5 value of 0.08, reflecting an intraspecies transmission rate 40 times higher than the interspecies rate. We leave γ r unchanged, resulting in an R w 0 = 0.57. We then ran the model with a fixed initial proportion of 10% infected reservoir hosts, matching the equilibrium proportion of infected wild animals, and simulated the spread of the pathogen through each intermediate host population. We 230 implemented a parameter sensitivity analysis for the reservoir species input parameters (see Table 7 Table 7 . The intermediate host species were ranked using an unweighted average of the maximum proportion of infected humans and the pathogen's global R 0 . We considered the maximum, rather than equilibrium, proportion of infected humans because a pathogen that peaks at a higher proportion of infected humans in its initial spillover population (such as the vendors at an animal mar-240 ket) has a higher chance of spreading among the human population generally even if it eventually reaches a lower equilibrium, and because in all our simulations a higher maximum proportion of infected humans implied a higher equilibrium proportion. The global R 0 , calculated for each potential intermediate host species using a next-generation matrix, is the maximum of the basic 245 reproduction of each strain in each species, and measures the epidemic spread in humans and animal populations, where the pathogen is assumed to mutate (see Royce and Fu, 2020 [18] , and Van den Driessche and Watmough, 2002 [31] ). In this framework, R 0 directly depends only on the similarity parameters, as these control the transmission rates. How-humans, the time to the epidemic peak in humans, and the equilibrium proportion of infected humans, although they do not always correspond to the most severe outbreak in the intermediate host species. We accurately identified palm civets as the most likely intermediate host produced an epidemic that infected more than 45% of susceptible humans or had an R 0 > 2 are summarized in Table 6 . Interestingly, they are all small carnivores or snakes. Table 5 . However, milk consumption is a valid possible factor for disease transmission to humans from a variety of animals, including camels, cows, donkeys, and goats, and we included these species in our analyses for all three coronaviruses. 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