An SEIHR model with age group and social contact for analysis of Fuzhou COVID-19 large wave

Abstract

Background: The structure of age groups and social contacts of the total population influenced infection scales and hospital-bed requirements, especially influenced severe infections and deaths during the global prevalence of COVID-19. Before the end of the year 2022, Chinese government implemented the national vaccination and had built the herd immunity cross the country, and announced Twenty Measures (November 11) and Ten New Measures (December 7) for further modifications of dynamic zero-COVID polity on the Chinese mainland. With the nation-wide vaccination and modified measures background, Fuzhou COVID-19 large wave (November 19, 2022-February 9, 2023) led by Omicron BA.5.2 variant was recorded and prevailed for three months in Fujian Province.

Methods: A multi-age groups susceptible-exposed-infected-hospitalized-recovered (SEIHR) COVID-19 model with social contacts was proposed in this study. The main object was to evaluate the impacts of age groups and social contacts of the total population. The idea of Least Squares method was governed to perform the data fittings of four age groups against the surveillance data from Fujian Provincial Center for Disease Control and Prevention (Fujian CDC). The next generation matrix method was used to compute basic reproduction number for the total population and for the specific age group. The tendencies of effective reproduction number of four age groups were plotted by using the Epiestim R package and the SEIHR model for in-depth discussions. The sensitivity analysis by using sensitivity index and partial rank correlation coefficients values (PRCC values) were operated to reveal the differences of age groups against the main parameters.

Results: The main epidemiological features such as basic reproduction number, effective reproduction number and sensitivity analysis were extensively discussed for multi-age groups SEIHR model in this study. Firstly, by using of the next generation matrix method, basic reproduction number R₀ of the total population was estimated as 1.57 using parameter values of four age groups of Fuzhou COVID-19 large wave. Given age group k, the values of R_0k (age group k to age group k), the values of $R_0^k$ (an infected of age group k to the total population) and the values of ${\hat{R}}_0^k$ (an infected of the total population to age group k) were also estimated, in which the explorations of the impacts of age groups revealed that the relationship $R_0^k>R_{0k}>{\hat{R}}_0^k$ was valid. Then, the fluctuating tendencies of effective reproduction number R_t were demonstrated by using two approaches (the surveillance data and the SEIHR model) for Fuzhou COVID-19 large wave, during which high-risk group (G4 group) mainly contributed the infection scale due to high susceptibility to infection and high risks to basic diseases. Further, the sensitivity analysis using two approaches (the sensitivity index and the PRCC values) revealed that susceptibility to infection of age groups played the vital roles, while the numerical simulation showed that infection scale varied with the changes of social contacts of age groups. The results of this study claimed that the high-risk group out of the total population was concerned by the local government with the highest susceptibility to infection against COVID-19.

Conclusions: This study verified that the partition structure of age groups of the total population, the susceptibility to infection of age groups, the social contacts among age groups were the important contributors of infection scale. The less social contacts and adequate hospital beds for high-risk group were profitable to control the spread of COVID-19. To avoid the emergence of medical runs against new variant in the future, the policymakers from local government were suggested to decline social contacts when hospital beds were limited.

Keywords: Age group; COVID-19 model; Contact matrix; Omicron BA.5.2 variant; Social contact.

Fig. 1

Vaccination situation of Fujian Province from November 1 to December 20 of the year 2022 against COVID-19. Full vaccination (Left top) and booster vaccination (Right top) are presented respectively. Vaccination situation of Fujian Province with the same scale-magnitude (Bottom).

Fig. 2

The heterogeneity of 16 × 16 contact matrix of the Chinese mainland was given in (Prem et al., 2021) (Left). The heterogeneity of 4 × 4 contact matrix of the Chinese mainland was computed by using the weighted average method (Right).

Fig. 3

The daily cases, cumulative cases and numerical simulations for four age groups of Fuzhou COVID-19 large wave. The daily cases with bars of the infected and the hospitalized came from the surveillance data of Fujian CDC. The cumulative cases in dashed curves and numerical simulations in solid curves were plotted for four age groups of Fuzhou COVID-19 large wave. The susceptibility to infection of age groups (λ_k) were changed twice starting from December 3 of the year 2022 with red dashed vertical line. The average hospitalization rates of age groups (θ_k) were changed on December 7 of the year 2022 with green dashed vertical line, which were consistent with the values and periods in Table B.3.

Fig. 4

Tendencies of effective reproduction number R_t for four age groups in Fuzhou COVID-19 large wave. The implements of Ten New Measures on December 7 brought the fluctuations of Fuzhou COVID-19 large wave. The rebounding tendency reached the peak after December 19 of the year 2022, Fuzhou COVID-19 large wave was controlled around January 12.

Fig. 5

The expression of $R_t^k$ for four age groups of Fuzhou COVID-19 large wave was given by formula (9). The value of $R_t^3$ for G3 group took the largest value during the implements of Twenty Measures. After the implements of Ten New Measures, both G3 group and G4 group took the high thresholds, G1 group and G2 group instead. Fuzhou COVID-19 large wave was controlled on the date ranging from December 25 to January 7 for each age group.

Fig. 6

The expression of R_t for the total population of Fuzhou COVID-19 large wave was given by formula (10). The threshold was above one during the implements of Twenty Measures and Ten New Measures, Fuzhou COVID-19 large wave was controlled on January 7.

Fig. 7

Local sensitivity analysis of R_0k with respect to the main parameters of the SEIHR model. The parameters λ_k, C_kk, θ_k and γ_1k had significant impacts on R_0k, using the formula log₁₀|Γ| for four age groups.

Fig. 8

Global sensitivity analysis: PRCC values for the peak numbers of the infected of four age groups. The sample size was set to be 3000. Parameter values and the values in contact matrix were provided in Table B.2 and Fig. 2b. (∗) denoted that the PRCCs were significant (p-value $<0.01$), among which the susceptibility to infection (λ_k), the incubation period (1/α) and aging rate (ω_k) of four age groups were significant.

Fig. 9

Scale scenario investigations for the hospitalized cases in G4 group. The surveillance data of the hospitalized for G4 group were from Fujian CDC in dashed curves on the left axis. The scale scenario simulations of the hospitalized for G4 group were in solid curves as presented on the right axis. The switchings for the susceptibility to infection (λ₄) in red dashed vertical line and the average hospitalization rates (θ₄) in green dashed vertical line were kept same with those of G4 group in Fig. 8 and Table B.3.