Natural history of influenza infection
Worldwide influenza pandemics have occurred at least three times in recorded history. The most serious pandemic is considered to have been the “Spanish flu” A (H1N1) in 1918–1919, which affected large parts of the world's population and was assessed to have killed at least 40 million people [14]. The much later “Asian flu” A (H2N2) in 1957–1958 and “Hong Kong flu” A (H3N2) in 1968–1969 also caused significant morbidity and mortality worldwide. To construct the model reported here, we used observational data from these previous pandemics for the latent and infectious periods, and illness attack and mortality rates as well as surveillance data for avian influenza A (H5N1) infection for the rate of crisis due to the unknown natural history of a future influenza infection.
Following the latent period, a person infected with influenza has infectivity during the infectious period; thereafter, he/she recovers with immunity or dies. The latent and infectious periods lasted 1–3 and 3–6 days with means of 1.9 and 4.1 days, respectively, in the “Asian flu” A (H2N2) [9], and the latent period ranged mainly from 1 to 4 days, with a maximum of 7 days for a few cases, in swine flu A (H1N1) in 2009 [15]. Based data on “Asian flu” A (H2N2), the latent and infectious periods were assumed to range over 1–3 and 3–6 days, respectively; the associated probabilities were tested at 30, 50, and 20%, and 30, 40, 20, and 10%, respectively.
Infected states were distinguished as symptomatic and asymptomatic infection. In this model, it was assumed that the rate of crisis was 67% on average, while the other cases were asymptomatic on the basis of the surveillance of avian influenza A (H5N1) infection [16], and that asymptomatic cases had half the infectivity of symptomatic cases [9]. A confirmative rate in all infections was defined by the ratio of patients who sought medical care and were diagnosed with a novel influenza. Because many cases of avian influenza A (H5N1) appeared to have severe symptoms with vomiting and diarrhea [17], the confirmative rate was assumed to be higher, at 60%.
The illness attack rate is different among different types of viruses [18], with that of the “Asian flu” A (H2N2) being much higher in children than in adults [19]; in contrast, the illness attack rate of the “Hong Kong flu” A (H3N2) was approximately the same among all age groups [20]. The illness attack rate of swine flu A (H1N1) virus has been reported to be twice as high in children as in adults [21]. A study of the sporadic transmissions of avian influenza A (H5N1) virus from birds to humans revealed that children are more susceptible to this virus than adults [2]. Because the age-specific illness attack rate of avian influenza A (H5N1) was similar to that of “Asian flu” A (H2N2) [22], this model adopted the estimated values in the “Asian flu” [10] as the age-specific illness attack rate. The mortality in “Spanish flu” A (H1N1) in 1918–1919 showed a W-shaped curve, i.e., it was high not among infants and elderly people but also among young adults (25–34 years), an age group which usually has a very low mortality with seasonal influenza [23, 24]. Although the profile for a future influenza pandemic is unclear, we assumed that a novel influenza infection would cause a high mortality similar to the situation of the “Spanish flu” A (H1N1) [24]. The age-specific illness attack and mortality rates in this model are presented in Table 1.
Table 1 Illness attack rate and mortality
Age (years) Illness attack rate (%)a Mortality (%)b
<1 32 2.25
1–4 0.70
5–14 46 0.16
15–24 0.60
25–34 29 1.00
35–44 0.58
45–54 0.32
55–64 0.42
65–74 0.67
75–84 1.20
>84 2.20
aRefer to [10]
bRefer to [24]
There are currently two kinds of antiviral drugs, oseltamivir and zanamivir, and both are regarded as being highly effective for both the treatment and prophylaxis of influenza infection [5, 25]. As treatment, a person must be treated with two tablets of oseltamivir a day for a course of 5 days for treatment; as prophylaxis, treatment consists of one tablet a day over a course of 7–10 days. Antiviral efficacy lasts only during the course, and no residual effect remains thereafter. The administration of antiviral drugs alleviates symptoms, reduces infectiveness, shortens the infectious period as a treatment effect, and also prevents infection as a prophylactical effect [26, 27]. Longini et al. [10] estimated the effects of administering the antiviral drugs that were also adopted in this model and found: (1) the illness attack rate in susceptible persons dosed with antiviral drugs for prophylaxis decreased to 0.30 on average compared with those without dosing (relative susceptibility = 0.30); (2) the probability of developing symptoms of influenza in infected persons dosed with antiviral drugs for prophylaxis decreased to 0.60 on average compared with those without dosing; (3) the infectiousness of infected persons dosed with antiviral drugs for treatment or prophylaxis decreased to 0.62 on average compared with those without dosing (relative infectiousness = 0.62); (4) the infectious period in infected persons dosed with antiviral drugs for treatment or prophylaxis was reduce to 1 day compared with those without dosing.