Archived Comments for:
A unified framework of immunological and epidemiological dynamics for the spread of viral infections in a simple network-based population
Page 4: "flow of free viral particles is proportional to the viral load of their neighbours" - I understand this model is an abstract one and understand the simplification it introduces, but I don't think it is correct epidemiologically since it should be a threshold function. It appears you note this as possible on page 12.
The basic observation about variance in immunological responsiveness appears to me to implement a kind of version of superspreading in your simplified contacts model.
The observation about the size of infecting dose affecting outcome doesn't seem right to me, although this may be because I am misinterpreting what is meant by the language used. The dose has an effect on whether or not the host gets infected, if it overwhelms the NK system. Isn’t it true that once a minimally infecting dose is achieved (perhaps representable as LD50) that can outreproduce the NK system's response and cause systemic (or major regional tissue) infection, that there is little relationship between dose and course? I believe it requires a large dose indeed to shorten the exponential growth curve for intra-host viral infections.
Aside from that, it wasn't entirely clear how many people were in the population - I saw 1,000, but is that correct? I'll note that in my modeling, I found that this size of population uniquely prevented herd immunity because the infection's life span allowed spread throughout the population before immunity could develop in any significant number of individuals. So there are threshold effects in population size for epidemics, and these may not be visible with certain approaches. I would tend to think of each element of this model as representing a group of individuals better than one individual.
Competing interests
I don't believe so. I have developed a model, but it does not compete with this one.
Authors' reply to: Nice, clear paper. A couple of thoughts.
David Vickers, Interdisciplinary Studies, College of Graduate Studies and Research, University of Saskatchewan, Saskatchewan, Canada.
6 January 2008
We appreciate Hanley’s thoughtful comments on the content of our paper published in the December 2007 issue of Theoretical Biology and Medical Modelling. While we welcome his constructive criticisms, his comments are evidence that some of the very general issues we discussed in the paper were not entirely clear. We hope the comments below will address Hanley’s stated concerns and clarify a few points about our results.
Firstly, our reference to "infecting dose" may have been a slight abuse of terminology and was not intended to be a representation of specific quantities such as an ID50, EID50, or LD50 frequently referenced in disciplines such as microbiology or immunology. Our use of the term "infecting dose" in the paper simply referred to the amount of virus with which an individual was infected with from their infected neighbours. We apologize for any confusion caused by our use of this term.
Secondly, immune responsiveness in this context was representative of an individual’s immuno-competency – reflecting the fact that at a certain point in time some people have a greater capacity to clear an infection than others. Although the effect of a super-spreader and someone with a low immune responsiveness may produce similar dynamics at the population level (i.e., they will both possess the ability to continually infect/re-infect others they are in contact with), we think that there are important characteristics – behavioural and otherwise – associated with a super-spreader that might distinguish them from those who are simply less "immuno-competent"; that is, although some super-spreaders may have low immune responsiveness, not all super-spreaders will share this characteristic.
Thirdly, infecting dose and course of clinical disease are somewhat independent, but have been reported to be correlated (reference 23 from our paper and references therein). In agreement with Hanley’s statement, a recent paper studying immune responses to influenza infections (Powell et. al. Clinical Microbiology 2006; 119: 87-94) demonstrated that, with the exception of very large doses of a virus, the timing of peak viral loads and clinical course of infection (recovery or death) will possess inconsequential differences.
In our paper, a similar outcome was demonstrated with the timing of peak viral load (see figure 10A within the index "case" – black lines). At this point however, we would like to make a distinction between the behaviour of the index case and that of secondary cases. For the index case, the initial level of viral load has relatively little effect on the severity of infection and on the timing of the peak viral load. By contrast, the initial viral load of the index case has a high degree of impact on the timing of the peak viral loads in the secondary cases. Interpretation of such changes in the course of infection for the secondary cases must, however, take into account that their initial viral load is identically zero for all "infecting dose" scenarios, and are infected via the index case. Viral loads in the secondary cases were functions of, not only, the initial viral load of the index case, but also of our assumptions about their immune responsiveness and the strength of their network connectivity. As a result, dynamic feedbacks from these characteristics may produce (sometimes counter-intuitive) behaviour. Still, it is also likely that the variation in the viral load of the secondary cases are artifacts of the details included in our model’s structure, and may qualitatively change when the model is calibrated to specific infections/diseases.
Lastly, the size of the simulated population, which throughout our paper was 1000 people, will affect the extent to which an infection (and disease) will spread to the rest of the population. However, the qualitative character of our results is not unique to this set of parameters we used. In fact, one of us (N.D.O.), in a separate publication, has demonstrated that the principle of similitude ensures that (dimensionally) similar results would be gained by a wide variety of population sizes, as long as parameter values were appropriately dimensionally scaled. While it is true that the course of infection spread in the population would, in general, vary with population size (given all other parameters are held equal), we would argue that the extent an infection will spread is also a function of many other factors, including (but not limited to) the level of epidemiological detail included in the model, the prevailing network topology, an individual’s immuno-competency, as well as the specific infection/disease being modelled. A self-limiting infection that "runs its course" before any of the defenses of the specific immune response can be mounted, and therefore before any immunological memory can be generated, might limit the prevalence of herd-immunity in a population.
One of the central goals of this paper was to study how immune reactions within individuals influence the overall nonlinear dynamics of an infection within a population of hosts. While we are grateful for Hanley’s comments, particularly for alerting us to some unclear aspects of our paper, we disagree with his last comment that each element of this model would better represent a group of people rather than a single individual.
Competing interests
Except for those in the pursuit of knowledge, we have no competing interests to declare.
Theoretical Biology and Medical Modelling
Nice, clear paper. A couple of thoughts.
22 December 2007
Page 4: "flow of free viral particles is proportional to the viral load of their neighbours" - I understand this model is an abstract one and understand the simplification it introduces, but I don't think it is correct epidemiologically since it should be a threshold function. It appears you note this as possible on page 12.
The basic observation about variance in immunological responsiveness appears to me to implement a kind of version of superspreading in your simplified contacts model.
The observation about the size of infecting dose affecting outcome doesn't seem right to me, although this may be because I am misinterpreting what is meant by the language used. The dose has an effect on whether or not the host gets infected, if it overwhelms the NK system. Isn’t it true that once a minimally infecting dose is achieved (perhaps representable as LD50) that can outreproduce the NK system's response and cause systemic (or major regional tissue) infection, that there is little relationship between dose and course? I believe it requires a large dose indeed to shorten the exponential growth curve for intra-host viral infections.
Aside from that, it wasn't entirely clear how many people were in the population - I saw 1,000, but is that correct? I'll note that in my modeling, I found that this size of population uniquely prevented herd immunity because the infection's life span allowed spread throughout the population before immunity could develop in any significant number of individuals. So there are threshold effects in population size for epidemics, and these may not be visible with certain approaches. I would tend to think of each element of this model as representing a group of individuals better than one individual.
Competing interests
I don't believe so. I have developed a model, but it does not compete with this one.
Authors' reply to: Nice, clear paper. A couple of thoughts.
6 January 2008
We appreciate Hanley’s thoughtful comments on the content of our paper published in the December 2007 issue of Theoretical Biology and Medical Modelling. While we welcome his constructive criticisms, his comments are evidence that some of the very general issues we discussed in the paper were not entirely clear. We hope the comments below will address Hanley’s stated concerns and clarify a few points about our results.
Firstly, our reference to "infecting dose" may have been a slight abuse of terminology and was not intended to be a representation of specific quantities such as an ID50, EID50, or LD50 frequently referenced in disciplines such as microbiology or immunology. Our use of the term "infecting dose" in the paper simply referred to the amount of virus with which an individual was infected with from their infected neighbours. We apologize for any confusion caused by our use of this term.
Secondly, immune responsiveness in this context was representative of an individual’s immuno-competency – reflecting the fact that at a certain point in time some people have a greater capacity to clear an infection than others. Although the effect of a super-spreader and someone with a low immune responsiveness may produce similar dynamics at the population level (i.e., they will both possess the ability to continually infect/re-infect others they are in contact with), we think that there are important characteristics – behavioural and otherwise – associated with a super-spreader that might distinguish them from those who are simply less "immuno-competent"; that is, although some super-spreaders may have low immune responsiveness, not all super-spreaders will share this characteristic.
Thirdly, infecting dose and course of clinical disease are somewhat independent, but have been reported to be correlated (reference 23 from our paper and references therein). In agreement with Hanley’s statement, a recent paper studying immune responses to influenza infections (Powell et. al. Clinical Microbiology 2006; 119: 87-94) demonstrated that, with the exception of very large doses of a virus, the timing of peak viral loads and clinical course of infection (recovery or death) will possess inconsequential differences.
In our paper, a similar outcome was demonstrated with the timing of peak viral load (see figure 10A within the index "case" – black lines). At this point however, we would like to make a distinction between the behaviour of the index case and that of secondary cases. For the index case, the initial level of viral load has relatively little effect on the severity of infection and on the timing of the peak viral load. By contrast, the initial viral load of the index case has a high degree of impact on the timing of the peak viral loads in the secondary cases. Interpretation of such changes in the course of infection for the secondary cases must, however, take into account that their initial viral load is identically zero for all "infecting dose" scenarios, and are infected via the index case. Viral loads in the secondary cases were functions of, not only, the initial viral load of the index case, but also of our assumptions about their immune responsiveness and the strength of their network connectivity. As a result, dynamic feedbacks from these characteristics may produce (sometimes counter-intuitive) behaviour. Still, it is also likely that the variation in the viral load of the secondary cases are artifacts of the details included in our model’s structure, and may qualitatively change when the model is calibrated to specific infections/diseases.
Lastly, the size of the simulated population, which throughout our paper was 1000 people, will affect the extent to which an infection (and disease) will spread to the rest of the population. However, the qualitative character of our results is not unique to this set of parameters we used. In fact, one of us (N.D.O.), in a separate publication, has demonstrated that the principle of similitude ensures that (dimensionally) similar results would be gained by a wide variety of population sizes, as long as parameter values were appropriately dimensionally scaled. While it is true that the course of infection spread in the population would, in general, vary with population size (given all other parameters are held equal), we would argue that the extent an infection will spread is also a function of many other factors, including (but not limited to) the level of epidemiological detail included in the model, the prevailing network topology, an individual’s immuno-competency, as well as the specific infection/disease being modelled. A self-limiting infection that "runs its course" before any of the defenses of the specific immune response can be mounted, and therefore before any immunological memory can be generated, might limit the prevalence of herd-immunity in a population.
One of the central goals of this paper was to study how immune reactions within individuals influence the overall nonlinear dynamics of an infection within a population of hosts. While we are grateful for Hanley’s comments, particularly for alerting us to some unclear aspects of our paper, we disagree with his last comment that each element of this model would better represent a group of people rather than a single individual.
Competing interests
Except for those in the pursuit of knowledge, we have no competing interests to declare.