Mathematical modeling of SARS: Cautious in all our movements

Hiroshi Nishiura, Theoretical Epidemiologist,
April 27, 2016

Dear Editor

Dr Bernard CK Choi and Dr Anita WP Pak recently developed a simple approximate mathematical model to predict the cumulative incidence and death.[1] Although it’s certainly easy to understand and to use as they stated, every users must be cautious about misunderstanding the real applications and evaluations for SARS epidemics. This problem originates in their too rough assumptions.

Firstly, since the model is based on simplification of an epidemic model, so called Kermack & McKendrick model,[2] the fate of an epidemic depends on threshold theorem: that is, R0 > 1 or not. They used a single value of the basic reproductive number, R0, throughout the epidemic. This, however, is not an accurate description of actual transmission dynamics because R0 is likely to decrease after the onset of an epidemic is detected and announced. Considering threshold host densities in case of simple circumstances,[3] R0 would be written as R0 = N/NT. Here N is the population size, and 1/NT is the proportionality constant whose value would be determined by all manner of biological, social, and environmental aspects of transmission. In the real SARS epidemic, the latter value might be largely affected by social reactions as well as environmental factors (including weather conditions as the authors mentioned). It is well known that the potentials for panic and social stigma are often much greater than the risk for the disease such as SARS. It is also notable that great variability in R0 should be a key to consider SARS epidemic. To say that a crude picture of SARS can be estimated with the model is quite different from saying that the model can be used to evaluate the success of interventions.

Secondly, as authors stated ‘may not’, homogenous mixing would not be a correct depiction of actual population interactions of SARS transmission. Although we are still in the face of so many unknowns including super-spreading events (SSEs), the small number of transmissions in most of the countries that experienced SARS occurrences suggests that the close contact required for transmission did not occur.[4] For instance, Japan has so far not experienced domestic transmission even though it had experienced the entrance of an SARS-CoV infected person, whereas one index case, not SSEs, caused an epidemic originated from Hospital in Toronto.[5] When we note that 76% of the infections in Singapore were acquired in a health-care facility,[6] it is evident SARS can easily be spread by close personal contact. Those facts were relatively known at that time when authors developed their model. Therefore, it is too optimistic to apply their assumption to the real data that every infected person will pass the disease to exactly R0 susceptible individuals.

I agree that user-friendly mathematical models must be developed and the mathematical models should be kept as simple as possible so that public health officers as well as students could predict and learn more effectively. Such models and recommendations for general usage, however, may send the wrong message to the local health officers and/or public. The models for the public must be based on clear knowledge, especially of epidemiological determinants and ecology of pathogens, when it comes to general usage. In order to avoid misleading, the mathematical epidemiologists cannot be too careful to describe their limitations of own models.

References

(1) Choi BCK, & Pak AWP. A simple approximate mathematical model to predict the number of SARS cases and deaths. J Epidem Com Health. 2003; In Press.

(2) Kermack WO, & McKendrick AG. Contributions to the mathematical theory of epidemics – 1927. R Stat Soc J 1927;115:700-721. (Reprinted in Bull Math Biol 1991;53:33-55).

(3) Anderson RM, & May RM. Infectious Diseases of Humans: Dynamics and Control. Oxford: Oxford University Press, 1992.

(4) Arita I, Kojima K, & Nakane M. Transmission of Severe Acute Respiratory Syndrome. Emerg Infect Dis 2003; 9: 1183-4.

(5) Dwosh HA, Hong HHL, Austgarden D, Herman S, & Schabas R. Identification and containment of an outbreak of SARS in a community hospital. CMAJ 2003; 168: 1415-20.

(6) Center for Disease Control and Prevention. Severe Acute Respiratory Syndrome-Singapore, 2003. MMWR 2003; 52: 405-11.

NOTE:Conflict of Interests including financial interests: Nil

None declared