Outbreak thresholds Beyond within Objective Describe some key processes that drive the ini6a6on and termina6on of infec6ous diseases in the ocean by a series of comprehensive dynamic models that yield the basic reproduc6on number R 0 . Beyond within Summary We propose a theore6cal basis for the transmission dynamics of marine infec6ous diseases (MIDs) by means of a series of compartmental models, expressed in a comprehensive formula6on adapted from Kermack and McKendrick's mathema6cal theory of epidemics. The models represent the dynamics of a variety of host‐pathogen systems including transmission by direct contact not only between live animals, but also between dead animals and living suscep6ble hosts. We also include cases where transmission occurs by environmental contact; that is, via par6cle transport through the water column and uptake by contact or filtra6on of waterborne infec6ve pathogens released to the water column by live or dead infected animals. From these models, we formulate the basic reproduc6on number R 0 using the next genera6on matrix procedure. The sensi6vity of the series of R 0 models to their parameters showed that, a priori, systems where the transmission involves a variety of processes, such as the death of infected animals, dead animals releasing pathogens in the water, and filter feeders accumula6ng them, an epizoo6c should be less probable than for contact‐based diseases for the same popula6on density. This is demonstrably not the case; thus, the rates of processes must also be increased considerably by these alterna6ve transmission pathways. This contribu6on covers the mathema6cal basis for the dynamics and epizoo6ology of a diverse array of MIDs, focusing on the ini6a6on and termina6on of epizoo6cs. Epizootiological modeling of marine infectious diseases G. Bidegain 1 , E.N. Powell 1 , J.M. Klinck 2 , T. Ben‐Horin 3 , E.E. Hofmann 2 1 Gulf Coast Research Lab, University of Southern Mississippi. 2 CCPO, Old Dominion University. 3 Haskin Shellfish Research Lab, Rutgers University. Project funded by the Na6onal Science Founda6on Evolu6on and Ecology Program,OCE‐1216220. Beyond within5.353.62 The model series scheme Key processes amplifying and diluting the disease risk Under certain conditions, high population filtration rates result in overfiltration in which water is filtered several times by neighboring individuals, thereby reducing the number of pathogens ingested and limiting disease outbreaks. R 0 <1 Extinction R 0 >1 Outbreak Surface level R 0 =1 Above R 0 >1 Below R 0 <1 High decay, dilution or advection of pathogens in the water (r) with respect to the release of pathogens (c), under conditions of high disease mortality or removal of dead infected animals, reduces the potential of epizootics. Systems with high transmission rates hamper the dilution of disease risk under these conditions. σ Γ F f P I c b I D m I S I D c b D β contact I S d D r P P P a F Γ Γ Model 8 Model 7 ϒ(sr Γ - sl P) σ Γ Model 6 Model 4 Model 3 Model 5 Model 1 Model 2 β particle P S β filtration f P S β filtration f P S ϒ(sr Γ - sl P) r P β contact D S Model 1: contact S and I, Model 2: contact S and D, Model 3: contact of P (from I) and S, Model 4: contact of P (from D) and S, Model 5: filtration of P form I, Model 6: filtration of P from D, Model 7: Model 5 + remote vol, Model 8: model 6 + remote vol. S=Susceptibles I=Infecteds D=Dead I P=local pool pathogens (water) F=Internal pathogens (population) Γ= remote pool β=transmission m=mortality d=Dead removal c=pathogen release b=pathogen body burden r=pathogen removal (water) f=filtration rate a=pathogen inactivation (internal) γ=pathogen exchange between pools σ= inactivation in R sl=1/Vl (local vol) sr=1/Vr(remote vol). 1.0 1.0 -1.0 -0.5 0.0 0.5 1.0 β N m d c b r f a γ σ sl sr Sensitivity Index -1.0 -0.5 0.0 0.5 1.0 β N m d c b r f a γ σ sl sr Sensitivity Index -1.0 -0.5 0.0 0.5 1.0 β N m d c b r f a γ σ sl sr Sensitivity Index -1.0 -0.5 0.0 0.5 1.0 β N m d c b r f a γ σ sl sr Sensitivity Index Model 1 Model 2 Model 3 Model 4 -1.0 -0.5 0.0 0.5 1.0 β N m d c b r f a γ σ sl sr Sensitivity Index -1.0 -0.5 0.0 0.5 1.0 β N m d c b r f a γ σ sl sr Sensitivity Index -1.0 -0.5 0.0 0.5 1.0 β N m d c b r f a γ σ sl sr Sensitivity Index -1.0 -0.5 0.0 0.5 1.0 β N m d c b r f a γ σ sl sr Sensitivity Index β N m d c b r f a γ σ sl sr β N m d c b r f a γ σ sl sr Parameters Parameters Model 6 Model 7 * * * * * * * Model 5 * * * * * Model 8 * * * * * * * * Sensitivity of R 0 models to parameters * Parameter with varying sensi6vity index depending on parameter values. Model 1 (m) Contact between Susceptible S and Infected individuals I Model 2 (d) Contact between Susceptible S and Dead Infected D Model 5 (fN/fN+r, m) Filtration of particles from I Model 6 (fN/fN+r, d) Filtration of particles from D Model 7 (V L , γ, m) Model 5 + remote volume Model 8 (V L , γ, d) Model 6 + remote volume Large remote volumes with a high transfer of pathogens between volumes (a diffusion‐like process) acts as a reservoir of pathogens diluting the disease risk. The initial population needed for an outbreak increases with increasing disease mortality rates (m) or removal of dead infected animals (d). However, this effect is much less important for host‐pathogen systems with high disease transmission rates. Model 3 (m) Contact between S and particles from I Model 4 (d) Contact between S and particles from D Remote Volume N = Initial susceptible population Haskin Shellfish Research Laboratory View publication stats View publication stats