We simulate the MSMH model over different time periods (i.e., 200-1000 years) to understand both the initial impact and long-term consequences of super-strains. We assume that initially there are neither infected pigs nor super-infected humans. In other words, an initial pre-epidemic period occurs before the super-strain emerges in humans, during which the avian and human strains can cocirculate in pigs for many years or even decades before a super-strain emerges in humans (Figs. ). The initial outbreak is abrupt once the super-strain emerges in humans and typically has the greatest magnitude. After a super-strain has emerged in humans, there are three possible epidemiological outcomes: periodic outbreaks (Figs. for approx. γp > 0.15); a super-strain that sustains at low levels without causing a significant outbreak (Figs. for approx. γp < 0.15); or a strong initial epidemic followed by weaker epidemics (Figs. ), where the super-strain replaces a previously circulating strain. The outcome is determined by transmissibility of the super-strain and the contact transmissibility from super-infectious pigs to humans. The time frame between the first two outbreaks ranges from 41 to 82 years, depending on the level of transmissibility (Fig. ).
Fig. 2 Time-series figures for the super-infectious humans at varying levels of interaction(A) The simulation illustrates that for low super-transmissibility (R0=1.4) and varying levels of interaction (γp), the system will exhibit reoccurring outbreaks. (more ...)
Fig. 3 Time between the first and second outbreaks at varying degrees of pig-to-human interaction The transmission of the super-strain in humans was set at five specific values. Time frames vary for βh,2=0.015 from 41 to 81 years (blue), βh,2 (more ...)
When the super-strain is not highly transmissible (i.e., less transmissible than seasonal flu) in humans, the super-strain can cause periodic epidemics in humans (Figs. ). For R0
= 1.4, periodic outbreaks occur at higher levels of pig-to-human contact transmissibility (approx. γp
> 0.15). In this case, we observe periodic epidemics in all population classes in both humans (Fig. ), and pigs (Fig. ). In addition, recombinant strains emerge in cycles (cyan: Fig. ). The oscillations in the number of coinfected pigs correlate with those of pigs infected with each separate strain (Fig. ). Super-infectious pigs attain a maximum number when pigs infected with the human strain are at a peak (cyan: Fig. ). Smaller outbreaks are more frequent with lower levels of interaction between pigs and humans, and larger but less frequent outbreaks occur at higher levels of interaction (Fig ). The periodicity of each strain will eventually stabilize, and outbreaks of both strains will occur abruptly after interepidemic periods of virtually no disease prevalence (red: Figs. . The time between the first two outbreaks ranges from approximately 55 to 81 years and is dependent on the transmissibility of the super-strain and pig-to-human contact transmissibility (Fig. : blue). These simulations show the reoccurring nature of pandemics (e.g., the three major outbreaks of the twentieth century: 1918, 1957, and 1968). It is worth noting that the 1918 virus spread between pigs and humans [24
]; however, it is unclear whether the virus initially spread from pig-to-human or human-to-pig.
Fig. 4 Simulation of the MSMH model for population densities versus time with high pig-to-human contact transmissibility and low super-strain transmissibility(A) The simulation for the humans. Colors represent densities over time of the susceptible (blue), primary (more ...)
At lower levels of transmission, we found that super-strains were continuously produced in the pig population, but only sustained at a low level (Figs. ) so they did not pose a threat to the human population. This example correlates to cases when the virus infects a few but is unable to establish itself after the initial outbreak, e.g., the “New Jersey” Incident in the USA in 1976 [25
] and perhaps other outbreaks involving a few individuals as described in [4
When the super-strain is highly transmissible (i.e., approximately as transmissible as 1918 flu, R0
=2.3), the strain will slowly emerge and cause an “epidemic spike” in humans (Figs. ). In this case, the resulting outbreak dynamics are influenced predominately by the high transmissibility of the super-strain. A series of dampening outbreaks follow the initial spike with periods of virtually no disease prevalence in humans between epidemic outbreaks. The super-strain outcompetes the preexisting endemic strain, causing the endemic strain to become extinct in humans and hence disappear from the pigs, eliminating the reoccurrence of coinfection and recombination. The time frame between the first two outbreaks ranges from approximately 61 to 69 years (Fig. : green). These simulations show features present in the pandemics of 1918, 1957, and 1968 in that after the initial pandemic the new super-strain displaces the previously dominant strain [26
], continues to circulate, and becomes endemic but with reduced epidemiological impact.
We compare both the epidemic magnitude and cumulative density for varying levels of pig-to-human contact transmissibility and super-strain transmission in humans. By analyzing the largest outbreak for approximately 75 years after the strain has emerged, we determine that a large scale epidemic will occur when 1.9 <R0 < 6.6; however, the greatest epidemic will occur when 2.3 <R0 < 3.8 (Fig. ) and not when R0 > 3.8. The contact transmissibility does not influence the magnitude of the largest outbreak but is a necessary component for the super-strain to emerge in humans. We determine that a significant outbreak is unlikely for R0 < 1.9 and a moderate outbreak will occur when R0 > 6.6. Furthermore, the most significant outbreaks (i.e., 2.3 < R0 < 3.8) occur when the super-strain is highly transmissible, and dampened outbreaks follow the large-scale epidemic (Figs. ). These results for the different values of R0 remain consistent for much longer time frames (e.g., 500 and 1000 years). Our results show that a super-strain that emerges from pigs to humans typically has the greatest potential for human mortalities during its initial outbreak.
Fig. 5 Contour maps of the pigs-to-human contact transmissibility (γp) versus the super-transmissibility in humans (βh,2)(A) The figure shows maximum number of super-strain over 200 years. The largest outbreaks occur when 2.3 <R0 < (more ...)
A similar analysis of cumulative (averaged annually) infections over different time frames shows higher levels of disease prevalence at lower levels of transmissibility. For 200 years, highest cumulative number occurs when 0 <R0 < 7.6 (Fig. : red-orange), of which there are two maximal states when 2.5 <R0 < 3.0 and 4.0 <R0 < 4.5 (Fig. : dark red). In this case, the cumulative number of infectives can be high even when R0 < 1.9 but depends on the pig-to-human contact transmissibility. For much longer time frames of 500 years (Fig. : dark red) and 1000 years (Fig. : dark red), the maximal prevalence occurs when: 1.9 <R0 < 3.0 for all levels of interaction, and R0 < 1.9 with a sufficient level of pig-to-human contact transmissibility. In fact, long-term prevalence is high even when R0 < 1 (βh,2 < 0.011) and the pig-to-human contact transmission is low (γp < 0.4, where the lower bound of γp is dependent on the value of R0). Furthermore, the epidemiological outcome can either be a large-scale outbreak or milder reoccurring outbreaks to sustain maximal prevalence of a super-strain.