Goffman and Newill1 have directed attention to the analogy between the spreading of an infectious disease and the dissemination of information. We have recently examined the spreading of a rumour from the point of view of mathematical epidemiology and wish to report very briefly here on work to be published in detail elsewhere2. In particular, we must emphasize that a mathematical model for the spreading of rumours can be constructed in a number of different ways, depending on the mechanism postulated to describe the growth and decay of the actual spreading process. In all these models the mathematical techniques familiar in mathematical epidemiology can be applied, but even the qualitative results so obtained need not necessarily be as expected on the basis of the formal analogy with epidemics.

Epidemics and Rumours

The understanding of the risk to humans from exposure to pathogens has been firmly put into a risk assessment framework. A key element of applying this approach is the understanding of the relationship between dose and response for particular pathogens. This understanding has progressed from early use of threshold concepts (“minimal infectious dose”) thru multiple generations of models. Generation 1 models describe probability of response to exposed dose. Generation 2 models incorporate host factors (e.g., age) and/or pathogen factors (e.g., particle size of inhaled agents). Generation 3 models describe the rate at which effects develop, i.e. the epidemic curve. These (generation 1 through three models) have been developed and used in multiple contexts. Beyond Generation 3 lies an opportunity for the deep incorporation of in vivo physiological responses and the coupling of the individual host dynamics to the dynamics of spread of contagious diseases in the population. This would enable more direct extrapo...

Microbial dose response modeling: past, present, and future.

While microbial risk assessment (MRA) has been used for over 25 years, traditional dose-response analysis has only predicted the overall risk of adverse consequences from exposure to a given dose. An important issue for consequence assessment from bioterrorist and other microbiological exposure is the distribution of cases over time due to the initial exposure. In this study, the classical exponential and beta-Poisson dose-response models were modified to include exponential-power dependency of time post inoculation (TPI) or its simplified form, exponential-reciprocal dependency of TPI, to quantify the time of onset of an effect presumably associated with the kinetics of in vivo bacterial growth. Using the maximum likelihood estimation approach, the resulting time-dose-response models were found capable of providing statistically acceptable fits to all tested pooled animal survival dose-response data. These new models can consequently describe the development of animal infectious response over time and represent observed responses fairly accurately. This is the first study showing that a time-dose-response model can be developed for describing infections initiated by various pathogens. It provides an advanced approach for future MRA frameworks.

Time‐Dose‐Response Models for Microbial Risk Assessment

Quantitative aspects of nuclear polyhedrosis virus infections in lepidopterous larvae: The dose-survival time relationship

Background: 21 days has been regarded as the appropriate quarantine period for holding individuals potentially exposed to Ebola Virus (EV) to reduce risk of contagion. There does not appear to be a systematic discussion of the basis for this period. Methods: The prior estimates for incubation time to EV were examined, along with data on the first 9 months of the current outbreak. These provided estimates of the distribution of incubation times. Results: A 21 day period for quarantine may result in the release of individuals with a 0.2 � 12% risk of release prior to full opportunity for the incubation to proceed. It is suggested that a detailed cost-benefit assessment, including considering full transmission risks, needs to occur in order to determine the appropriate quarantine period for potentially exposed individuals. Abstract Background: 21 days has been regarded as the appropriate quarantine period for holding individuals potentially exposed to Ebola Virus (EV) to reduce risk of contagion. There does not appear to be a systematic discussion of the basis for this period. Methods: The prior estimates for incubation time to EV were examined, along with data on the first 9 months of the current outbreak. These provided estimates of the distribution of incubation times. Results: A 21 day period for quarantine may result in the release of individuals with a 0.2 � 12% risk of release prior to full opportunity for the incubation to proceed. It is suggested that a detailed cost-benefit assessment, including considering full transmission risks, needs to occur in order to determine the appropriate quarantine period for potentially exposed individuals. Abstract Background: 21 days has been regarded as the appropriate quarantine period for holding individuals potentially exposed to Ebola Virus (EV) to reduce risk of contagion. There does not appear to be a systematic discussion of the basis for this period. Methods: The prior estimates for incubation time to EV were examined, along with data on the first 9 months of the current outbreak. These provided estimates of the distribution of incubation times. Results: A 21 day period for quarantine may result in the release of individuals with a 0.2 � 12% risk of release prior to full opportunity for the incubation to proceed. It is suggested that a detailed cost-benefit assessment, including considering full transmission risks, needs to occur in order to determine the appropriate quarantine period for potentially exposed individuals.

/pdf/on-the-quarantine-period-for-ebola-virus-ufc1s99o7t.pdf

On the Quarantine Period for Ebola Virus

The Basic Birth‐Death Model for Microbial Infections

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The Basic Birth‐Death Model for Microbial Infections