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Variants of the susceptible-infected-removed (SIR) model of Kermack & McKendrick (1927) enjoy wide application in epidemiology, offering simple yet powerful inferential and predictive tools in the study of diverse infectious diseases across human, animal and plant populations. Direct transmission models (DTM) are a subset of these that treat the processes of disease transmission as comprising a series of discrete instantaneous events. Infections transmitted indirectly by persistent environmental pathogens, however, are examples where a DTM description might fail and are perhaps better described by models that comprise explicit environmental transmission routes, so-called environmental transmission models (ETM). In this paper we discuss the stochastic susceptible-exposed-infected-removed (SEIR) DTM and susceptible-exposed-infected-removed-pathogen (SEIR-P) ETM and we show that the former is the timescale separation limit of the latter, with ETM host-disease dynamics increasingly resembling those of a DTM when the pathogen's characteristic timescale is shortened, relative to that of the host population. Using graphical posterior predictive checks (GPPC), we investigate the validity of the SEIR model when fitted to simulated SEIR-P host infection and removal times. Such analyses demonstrate how, in many cases, the SEIR model is robust to departure from direct transmission. Finally, we present a case study of white spot disease (WSD) in penaeid shrimp with rates of environmental transmission and pathogen decay (SEIR-P model parameters) estimated using published results of experiments. Using SEIR and SEIR-P simulations of a hypothetical WSD outbreak management scenario, we demonstrate how relative shortening of the pathogen timescale comes about in practice. With atttempts to remove diseased shrimp from the population every 24h, we see SEIR and SEIR-P model outputs closely conincide. However, when removals are 6-hourly, the two models' mean outputs diverge, with distinct predictions of outbreak size and duration. Author summary: Mathematical models of the spread and progression of communicable disease in populations are important tools in efforts to prevent and control outbreaks. A common class of disease models assume that infection is transmitted directly from infectious to susceptible individuals when they are in close proximity—so called direct transmission models. These are used widely and have proven invaluable as simplified descriptions of a wide array of infectious diseases in diverse populations. However, many pathogens spread through indirect, environmental routes of transmission, for example via contact with contaminated water sources in the case of cholera, or inhalation of infectious airborne droplets for respiratory infections, such as Covid-19. We show that direct transmission models work well for such pathogens with short environmental lifetimes and where hosts shed pathogens into the environment at high rates. This means that we do not require information about environmental pathogen levels to understand the behaviour of outbreaks caused by these pathogens. When shedding rates are also low, e.g., with macroparasitic infections, or when variable environmental factors play a role in transmissibility, then explicit modelling of both the pathogen and environmental transmission will provide a more accurate picture than a direct transmission approximation. [ABSTRACT FROM AUTHOR]

Gyrodactylus salaris (Monogenea, Platyhelminthes) is a notifiable freshwater pathogen responsible for causing catastrophic damage to wild Atlantic salmon stocks, most notably in Norway. In some strains of Baltic salmon (e.g., from the river Neva) however, the impact is greatly reduced due to some form of innate resistance that regulates parasite numbers, resulting in fewer host mortalities. Gyrodactylus salaris is known from 17 European states; its status in a further 35 states remains unknown; the UK, the Republic of Ireland and certain watersheds in Finland are free of the parasite. Thus, the parasite poses a serious threat if it emerges in Atlantic salmon rearing regions throughout Europe. At present, infections are generally controlled via extreme measures such as the treatment of entire river catchments with the biocide rotenone, in order to remove all hosts, before restocking with the original genetic stock. The use of rotenone in this way in EU countries is unlikely as it would be in contravention of the Water Framework Directive. Not only are such treatments economically and environmentally costly, they also eradicate the potential for any host/parasite evolutionary process to occur. Based on previous studies, UK salmon stocks have been shown to be highly susceptible to infection, analogous to Norwegian stocks. The present study investigates the impact of a G. salaris outbreak within a naïve salmon population in order to determine long-term consequences of infection and the likelihood of coexistence. Simulation of the salmon/ G. salaris system was carried out via a deterministic mathematical modelling approach to examine the dynamics of host-pathogen interactions. Results indicated that in order for highly susceptible Atlantic strains to evolve a resistance, both a moderate-strong deceleratingly costly trade-off on birth rate and a lower overall cost of the immune response are required. The present study provides insights into the potential long term impact of G. salaris if introduced into G. salaris-free territories and suggests that in the absence of external controls salmon populations are likely to recover to high densities nearing 90% of that observed pre-infection. [ABSTRACT FROM AUTHOR]

Gyrodactylus salaris is a notifiable freshwater ectoparasite of salmonids. Its primary host is Atlantic salmon (Salmo salar), upon which infections can cause death, and have led to massive declines in salmon numbers in Norway, where the parasite is widespread. Different strains of S. salar vary in their susceptibility, with Atlantic strains (such as those found in Norway) exhibiting no resistance to the parasite, and Baltic strains demonstrating an innate resistance sufficient to regulate parasite numbers on the host causing it to either die out or persist at a low level. In this study, Leslie matrix and compartmental models were used to generate data that demonstrated the population growth of G. salaris on an individual host is dependent on the total number of offspring per parasite, its longevity and the timing of its births. The data demonstrated that the key factor determining the rate of G. salaris population growth is the time at which the parasite first gives birth, with rapid birth rate giving rise to large population size. Furthermore, it was shown that though the parasite can give birth up to four times, only two births are required for the population to persist as long as the first birth occurs before a parasite is three days old. As temperature is known to influence the timing of the parasite's first birth, greater impact may be predicted if introduced to countries with warmer climates than Norway, such as the UK and Ireland which are currently recognised to be free of G. salaris. However, the outputs from the models developed in this study suggest that temperature induced trade-offs between the total number of offspring the parasite gives birth to and the first birth timing may prevent increased population growth rates over those observed in Norway. [ABSTRACT FROM AUTHOR]

Gyrodactylus salaris is a notifiable freshwater ectoparasite of salmonids. Its primary host is Atlantic salmon (Salmo salar), upon which infections can cause death, and have led to massive declines in salmon numbers in Norway, where the parasite is widespread. Different strains of S. salar vary in their susceptibility, with Atlantic strains (such as those found in Norway) exhibiting no resistance to the parasite, and Baltic strains demonstrating an innate resistance sufficient to regulate parasite numbers on the host causing it to either die out or persist at a low level. In this study, Leslie matrix and compartmental models were used to generate data that demonstrated the population growth of G. salaris on an individual host is dependent on the total number of offspring per parasite, its longevity and the timing of its births. The data demonstrated that the key factor determining the rate of G. salaris population growth is the time at which the parasite first gives birth, with rapid birth rate giving rise to large population size. Furthermore, it was shown that though the parasite can give birth up to four times, only two births are required for the population to persist as long as the first birth occurs before a parasite is three days old. As temperature is known to influence the timing of the parasite's first birth, greater impact may be predicted if introduced to countries with warmer climates than Norway, such as the UK and Ireland which are currently recognised to be free of G. salaris. However, the outputs from the models developed in this study suggest that temperature induced trade-offs between the total number of offspring the parasite gives birth to and the first birth timing may prevent increased population growth rates over those observed in Norway.