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

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 R0k (age group k to age group k), the values of R0k (an infected of age group k to the total population) and the values of R^0k (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 R0k>R0k>R^0k was valid. Then, the fluctuating tendencies of effective reproduction number Rt 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.

Epidemiological feature analysis of SVEIR model with control strategy and variant evolution.

The complex interactions were performed among non-pharmaceutical interventions, vaccinations, and hosts for all epidemics in mainland China during the spread of COVID-19. Specially, the small-scale epidemic in the city described by SVEIR model was less found in the current studies. The SVEIR model with control was established to analyze the dynamical and epidemiological features of two epidemics in Jinzhou City led by Omicron variants before and after Twenty Measures. In this study, the total population (N) of Jinzhou City was divided into five compartments: the susceptible (S), the vaccinated (V), the exposed (E), the infected (I), and the recovered (R). By surveillance data and the SVEIR model, three methods (maximum likelihood method, exponential growth rate method, next generation matrix method) were governed to estimate basic reproduction number, and the results showed that an increasing tendency of basic reproduction number from Omicron BA.5.2 to Omicron BA.2.12.1. Meanwhile, the effective reproduction number for two epidemics were investigated by surveillance data, and the results showed that Jinzhou wave 1 reached the peak on November 1 and was controlled 7 days later, and that Jinzhou wave 2 reached the peak on November 28 and was controlled 5 days later. Moreover, the impacts of non-pharmaceutical interventions (awareness delay, peak delay, control intensity) were discussed extensively, the variations of infection scales for Omicron variant and EG.5 variant were also discussed. Furthermore, the investigations on peaks and infection scales for two epidemics in dynamic zero-COVID policy were operated by the SVEIR model with control. The investigations on public medical requirements of Jinzhou City and Liaoning Province were analyzed by using SVEIR model without control, which provided a possible perspective on variant evolution in the future.

Transmission dynamics of symptom-dependent HIV/AIDS models.

In this study, we proposed two, symptom-dependent, HIV/AIDS models to investigate the dynamical properties of HIV/AIDS in the Fujian Province. The basic reproduction number was obtained, and the local and global stabilities of the disease-free and endemic equilibrium points were verified to the deterministic HIV/AIDS model. Moreover, the indicators $ R_0/ $ and $ R_0^e $ were derived for the stochastic HIV/AIDS model, and the conditions for stationary distribution and stochastic extinction were investigated. By using the surveillance data from the Fujian Provincial Center for Disease Control and Prevention, some numerical simulations and future predictions on the scale of HIV/AIDS infections in the Fujian Province were conducted.

COVID-19 transmission driven by age-group mathematical model in Shijiazhuang City of China.

Background: A COVID-19 outbreak in the rural areas of Shijiazhuang City was attributed to the complex interactions among vaccination, host, and non-pharmaceutical interventions (NPIs). Herein, we investigated the epidemiological characteristics of all reported symptomatic cases by picking Shijiazhuang City, Hebei Province in Northern China as research objective. In addition, we established a with age-group mathematical model to perform the optimal fitting and to investigate the dynamical profiles under three scenarios. Methods: All reported symptomatic cases of Shijiazhuang epidemic (January 2-February 3, 2021) were investigated in our study. The cases were classified by gender, age group and location, the distributions were analyzed by epidemiological characteristics. Furthermore, the reported data from Health Commission of Hebei Province was also analyzed by using an age-group mathematical model by two phases and three scenarios. Results: Shijiazhuang epidemic caused by SARS-CoV-2 wild strain was recorded with the peak 84 cases out of 868 reported symptomatic cases on January 11, 2021, which was implemented with strong NPIs by local government and referred as baseline situation in this study. The research results showed that R0 under baseline situation ranged from 4.47 to 7.72, and Rt of Gaocheng Distinct took 3.72 with 95% confidence interval from 3.23 to 4.35 on January 9, the declining tendencies of Rt under baseline situation were kept till February 3, the value of Rt reached below 1 on January 19 and remained low value up to February 3 for Gaocheng District and Shijiazhuang City during Shijiazhuang epidemic. This indicated Shijiazhuang epidemic was under control on January 19. However, if the strong NPIs were kept, but remote isolation operated on January 11 was not implemented as of February 9, then the scale of Shijiazhuang epidemic reached 9482 cases from age group who were 60 years old and over out of 31,017 symptomatic cases. The investigation also revealed that Shijiazhuang epidemic reached 132,648 symptomatic cases for age group who were 60 years old and over (short for G2) under risk-based strategies (Scenario A), 58,048 symptomatic cases for G2 under late quarantine strategies (Scenario B) and 207,124 symptomatic cases for G2 under late quarantine double risk strategies (Scenario C), and that the corresponding transmission tendencies of Rt for three scenarios were consistently controlled on Jan 29, 2021. Compared with baseline situation, the dates for controlling Rt below 1 under three scenarios were delayed 10 days. Conclusions: Shijiazhuang epidemic was the first COVID-19 outbreak in the rural areas in Hebei Province of Northern China. The targeted interventions adopted in early 2021 were effective to halt the transmission due to the implementation of a strict and village-wide closure. However we found that age group profile and NPIs played critical rules to successfully contain Shijiazhuang epidemic, which should be considered by public health policies in rural areas of mainland China during the dynamic zero-COVID policy.

Survival analysis and probability density function of switching heroin model.

We study a switching heroin epidemic model in this paper, in which the switching of supply of heroin occurs due to the flowering period and fruiting period of opium poppy plants. Precisely, we give three equations to represent the dynamics of the susceptible, the dynamics of the untreated drug addicts and the dynamics of the drug addicts under treatment, respectively, within a local population, and the coefficients of each equation are functions of Markov chains taking values in a finite state space. The first concern is to prove the existence and uniqueness of a global positive solution to the switching model. Then, the survival dynamics including the extinction and persistence of the untreated drug addicts under some moderate conditions are derived. The corresponding numerical simulations reveal that the densities of sample paths depend on regime switching, and larger intensities of the white noises yield earlier times for extinction of the untreated drug addicts. Especially, when the switching model degenerates to the constant model, we show the existence of the positive equilibrium point under moderate conditions, and we give the expression of the probability density function around the positive equilibrium point.

Study on the COVID-19 epidemic in mainland China between November 2022 and January 2023, with prediction of its tendency.

The prediction system EpiSIX was used to study the COVID-19 epidemic in mainland China between November 2022 and January 2023, based on reported data from December 9, 2022, to January 30, 2023, released by The Chinese Center for Disease Control and Prevention on February 1, 2023. Three kinds of reported data were used for model fitting: the daily numbers of positive nucleic acid tests and deaths, and the daily number of hospital beds taken by COVID-19 patients. It was estimated that the overall infection rate was 87.54% and the overall case fatality rate was 0.078%-0.116% (median 0.100%). Assuming that a new COVID-19 epidemic outbreak would start in March or April of 2023, induced by a slightly more infectious mutant strain, we predicted a possible large rebound between September and October 2023, with a peak demand of between 800,000 and 900,000 inpatient beds. If no such new outbreak was induced by other variants, then the current COVID-19 epidemic course in mainland China would remain under control until the end of 2023. However, it is suggested that the necessary medical resources be prepared to manage possible COVID-19 epidemic emergencies in the near future, especially for the period between September and October 2023.

Study and prediction of the 2022 global monkeypox epidemic.

The World Health Organization (WHO) declared monkeypox as a public health emergency of international concern (PHEIC) on July 23, 2022, their highest level of alert. This raised concerns about the management of the global monkeypox outbreak, as well as the scientific analysis and accurate prediction of the future course of the epidemic. This study used EpiSIX (an analysis and prediction system for epidemics based on a general SEIR model) to analyze the monkeypox epidemic and to forecast the major tendencies based on data from the USA CDC (https://www.cdc.gov) and the WHO (https://www.who.int/health-topics/monkeypox). The global outbreak of monkeypox started in the UK on May 2, 2022, which marked the beginning of an epidemic wave. As of October 28, 2022, the cumulative number of reported cases worldwide was 77,115, with 36 deaths. EpiSIX simulations predict that the global monkeypox epidemic will enter a low epidemic status on March 1, 2023 with the cumulative number of confirmed cases ranging from 85,000 to 124,000, and the total number of deaths ranging from 60 to 87. Our analysis revealed that the basic reproduction number (R0) of monkeypox virus (MPXV) is near to 3.1 and the percentage of asymptomatic individuals is 13.1 %-14.5 %, both of which are similar to the data for SARS. The vaccination efficiency against susceptibility (VEs) of individuals who have had monkeypox is âˆ¼ 79 %, and the vaccination efficiency against infectiousness (VEi) of individuals who have had monkeypox is âˆ¼ 76 %-82 %. The mean incubation period for monkeypox is 8 days. In total, 94.7 % of infected individuals develop symptoms within 20 days and recover within 2 weeks after the confirmation of symptoms. Simulation results using EpiSIX showed that ring vaccination was remarkably effective against monkeypox. Our findings confirmed that a 20-day isolation for close contacts is necessary.

Single-species population models with stage structure and partial tolerance in polluted environments.

We propose stage-structured single-species population models with psychological effects and partial tolerance in polluted environments in this paper. First, the conditions of extinction and the time for extinction are investigated respectively. Especially, the time for extinction takes longer as the value of the psychological effects increases. Then the weak persistence in the mean around the pollution-free equilibrium and the stochastic permanence have been derived under some moderate conditions. Further, the existence of a periodic solution for the periodic single-species population has been determined. The corresponding numerical simulations verify the efficiency of the main theoretical results.

Impact of "blocking" structure in the troposphere on the wintertime persistent heavy air pollution in northern China.

In the winters of 2012-2018, a total of 25 'ultra-long' (≥6 days), wide-ranging pollution events occurred in northern China. The results showed that the atmospheric circulation pattern corresponding to 62.5% of the persistent 'most serious' and 'more serious' air pollution events in northern China were the blocking structures, and that 43.75% of the 500-hPa atmospheric circulation anomalies in the middle and high latitudes of Eurasia were 'dual-blocking', 18.75% of them were 'single-blocking'. The abnormally stable blocking situation provided a special circulation background for the occurrence and maintenance of persistent heavy air pollution in northern China. The Okhotsk blocking is significantly positively correlated with the persistent 'most serious' air pollution events. 'Stagnation' of the blocking system and its dynamic effect play an important role in regulating atmospheric environmental capacity and accelerating the accumulation of aerosols during the persistent heavy pollution episodes. Due to the synergy between the weak wind effect of the leeward slope on the eastern side of the Loess Plateau in this region and the downward airflow of the large-scale blocking system, the effect of sustained suppression of atmospheric pollutant diffusion in northern China is more significant. The downward air flow along the eastern leeward slope of the Loess Plateau is very important for accumulation of air pollutants, which is controlled by the tropospheric blocking high. In addition, the 'subsidence (temperature) inversion' effect produced by the synergy between the downward airflow of the eastern leeward slope of the Loess Plateau and the large-scale blocking system creates a continuous and stable 'warm-cover' structure in the middle of the troposphere on the eastern of the Loess Plateau; this effect strengthens the radiation effect of aerosols in the atmospheric pollutants, as well as the 'two-way feedback' mechanism between adverse meteorological conditions in the boundary layer and atmospheric pollutants.

Psychological effect on single-species population models in a polluted environment.

We formulate and investigate the psychological effect of single-species population models in a polluted environment in this paper. For the deterministic single-species population model, the conditions that guarantee the local extinction and persistence in the mean are derived firstly. We then show that, around the pollution-free equilibrium, the stochastic single-species population is weakly persistent in the mean, and is stochastically permanent under some conditions. As a consequence, some numerical simulations demonstrate the efficiency of the main results.

Genetic diversity of Guangxi chicken breeds assessed with microsatellites and the mitochondrial DNA D-loop region.

The domestic chicken (Gallus gallus domesticus) is an excellent model for genetic studies of phenotypic diversity. The Guangxi Region of China possesses several native chicken breeds displaying a broad range of phenotypes well adapted to the extreme hot-and-wet environments in the region. We thus evaluated the genetic diversity and relationships among six native chicken populations of the Guangxi region and also evaluated two commercial breeds (Arbor Acres and Roman chickens). We analyzed the sequences of the D-loop region of the mitochondrial DNA (mtDNA) and 18 microsatellite loci of 280 blood samples from six Guangxi native chicken breeds and from Arbor Acres and Roman chickens, and used the neighbor-joining method to construct the phylogenetic tree of these eight breeds. Our results showed that the genetic diversity of Guangxi native breeds was relatively rich. The phylogenetic tree using the unweighed pair-group method with arithmetic means (UPGAM) on microsatellite marks revealed two main clusters. Arbor Acres chicken and Roman chicken were in one cluster, while the Guangxi breeds were in the other cluster. Moreover, the UPGAM tree of Guangxi native breeds based on microsatellite loci was more consistent with the genesis, breeding history, differentiation and location than the mtDNA D-loop region. STRUCTURE analysis further confirmed the genetic structure of Guangxi native breeds in the Neighbor-Net dendrogram. The nomenclature of mtDNA sequence polymorphisms suggests that the Guangxi native chickens are distributed across four clades, but most of them are clustered in two main clades (B and E), with the other haplotypes within the clades A and C. The Guangxi native breeds revealed abundant genetic diversity not only on microsatellite loci but also on mtDNA D-loop region, and contained multiple maternal lineages, including one from China and another from Europe or the Middle East.