Effect of the one-child policy on influenza transmission in China: a stochastic transmission model

Abstract

Background: China's one-child-per-couple policy, introduced in 1979, led to profound demographic changes for nearly a quarter of the world's population. Several decades later, the consequences include decreased fertility rates, population aging, decreased household sizes, changes in family structure, and imbalanced sex ratios. The epidemiology of communicable diseases may have been affected by these changes since the transmission dynamics of infectious diseases depend on demographic characteristics of the population. Of particular interest is influenza because China and Southeast Asia lie at the center of a global transmission network of influenza. Moreover, changes in household structure may affect influenza transmission. Is it possible that the pronounced demographic changes that have occurred in China have affected influenza transmission?

Methods and findings: To address this question, we developed a continuous-time, stochastic, individual-based simulation model for influenza transmission. With this model, we simulated 30 years of influenza transmission and compared influenza transmission rates in populations with and without the one-child policy control. We found that the average annual attack rate is reduced by 6.08% (SD 2.21%) in the presence of the one-child policy compared to a population in which no demographic changes occurred. There was no discernible difference in the secondary attack rate, -0.15% (SD 1.85%), between the populations with and without a one-child policy. We also forecasted influenza transmission over a ten-year time period in a population with a two-child policy under a hypothesis that a two-child-per-couple policy will be carried out in 2015, and found a negligible difference in the average annual attack rate compared to the population with the one-child policy.

Conclusions: This study found that the average annual attack rate is slightly lowered in a population with a one-child policy, which may have resulted from a decrease in household size and the proportion of children in the population.

Figure 1. Progression of the model.

Given a time t, each individual in the model is in one state of (susceptible), (mild exposure), (not mild exposure), (mild asymptomatic infectiousness), (not mild asymptomatic infectiousness), (symptomatic infectiousness) and (recovered with immunity), and the population's inflow and outflow are represented by each individual's age-specific death rate d and age-specific fertility rate b.

Figure 2. Dynamic Network Structure.

The population contact network of this model consists of every individual's household, school (if in school age) and casual links. This small part of the network has 13 individuals in 5 households with different sizes: individual a is in a 1-member household, individuals l and m are in a 2-member household, individuals b, c and d, and individuals i, j and k are in two 3-member households, individuals e, f, g and h are in a 4-member household. Individuals in each household are linked each other by thick lines. Each individual has some casual links (linked by thin lines) to other non-household members. School age individuals b, f, i, j, h and l are in two different schools and linked by dotted lines (the schoolmate relationship). Individual b has two household members (c and d), two visible casual contacts (a and e), and three visible schoolmates (f, i and j), other social contacts and schoolmates of b are not shown in this small part of contact network. If b was an index case, the household contacts would be at highest risk of being infected due to the higher contact rates among household members than the casual and school contacts (for the contact rates of different link types, please see Table 2).

Figure 3. AR and SAR differences between populations without the one-child policy and with the one-child policy.

(A) Average difference in annual attack rate (ΔAR: 6.08% (SD 2.21%)) between populations without the one-child policy and with the one-child policy, based on 646 calibrated parameter sets which yielded the annual attack rates between 10% and 20%, and secondary attack rates between 9% and 32%. For each parameter set, we simulated the influenza trajectories under two demographic control policies, and then computed the difference in average annual attack rates over 30 years between two policies. (B) Difference in secondary attack rates (ΔSAR: −0.15% (SD 1.85%)) between populations without one-child policy and with the child-policy, based on 646 calibrated parameter sets which yielded the annual attack rates between 10% and 20%, and the secondary attack rates between 9% and 32%. For each parameter set, we simulated the influenza trajectories under two demographic control policies, and then computed the difference in average secondary attack rates over 30 years between two policies.

Figure 4. AR and SAR differences between one-child policy and two-child policy (10 years: 2015 to 2024).

(A) ΔAR (0.22% (SD 0.46%)) between one-child and two-child policies based on 646 calibrated parameter sets which yielded the annual attack rates between 10% and 20% and the secondary attack rates between 9% and 32%. For each parameter set, we simulated the influenza trajectories under two demographic control policies, and then computed the difference in average annual attack rates over 10 years (2015 to 2024) between two policies. (B) ΔSAR (−0.02% (SD 0.81%)) between one-child and two-child policies based on 646 calibrated parameter sets which yielded the annual attack rates between 10% and 20% and the secondary attack rates between 9% and 32%. For each parameter set, we simulated the influenza trajectories under two demographic control policies, and then computed the difference in average secondary attack rates over 10 years (2015 to 2024) between two policies.

Figure 5. AR and SAR differences under assumptions of different contact and immunity loss rates.

(A) Varying the value of contact rate per day between any two members in a household (from 12 to 20) and the value of immunity loss rate per year (from 20% to 100%) yielded that under the scenario of 12 of household contact rate and 100% of immunity loss per year, the AR in the population without the one-child policy could be 60% higher than the AR in the population with the one-child policy. (B) By varying the values of contact rate per day between any two members in a household (from 12 to 20) and the immunity loss rate per year (from 20% to 100%), the SAR in the population without one-child policy could be 3% higher than the SAR in the population without the one-child policy, when the contact rate per day in household is 12 and the immunity loss rate per year is 80%.