Mathematical Models Supporting Control of COVID-19.

Mathematical models have played an important role in the management of the coronavirus disease 2019 (COVID-19) pandemic. The aim of this review is to describe the use of COVID-19 mathematical models, their classification, and the advantages and disadvantages of different types of models. We conducted subject heading searches of PubMed and China National Knowledge Infrastructure with the terms "COVID-19," "Mathematical Statistical Model," "Model," "Modeling," "Agent-based Model," and "Ordinary Differential Equation Model" and classified and analyzed the scientific literature retrieved in the search. We categorized the models as data-driven or mechanism-driven. Data-driven models are mainly used for predicting epidemics, and have the advantage of rapid assessment of disease instances. However, their ability to determine transmission mechanisms is limited. Mechanism-driven models include ordinary differential equation (ODE) and agent-based models. ODE models are used to estimate transmissibility and evaluate impact of interventions. Although ODE models are good at determining pathogen transmission characteristics, they are less suitable for simulation of early epidemic stages and rely heavily on availability of first-hand field data. Agent-based models consider influences of individual differences, but they require large amounts of data and can take a long time to develop fully. Many COVID-19 mathematical modeling studies have been conducted, and these have been used for predicting trends, evaluating interventions, and calculating pathogen transmissibility. Successful infectious disease modeling requires comprehensive considerations of data, applications, and purposes.

Assessing the Impacts of Meteorological Factors on COVID-19 Pandemic Using Generalized Estimating Equations

Background Meteorological factors have been proven to affect pathogens;both the transmission routes and other intermediate. Many studies have worked on assessing how those meteorological factors would influence the transmissibility of COVID-19. In this study, we used generalized estimating equations to evaluate the impact of meteorological factors on Coronavirus disease 2019 (COVID-19) by using three outcome variables, which are transmissibility, incidence rate, and the number of reported cases. Methods In this study, the data on the daily number of new cases and deaths of COVID-19 in 30 provinces and cities nationwide were obtained from the provincial and municipal health committees, while the data from 682 conventional weather stations in the selected provinces and cities were obtained from the website of the China Meteorological Administration. We built a Susceptible-Exposed-Symptomatic-Asymptomatic-Recovered/Removed (SEIAR) model to fit the data, then we calculated the transmissibility of COVID-19 using an indicator of the effective reproduction number (Reff). To quantify the different impacts of meteorological factors on several outcome variables including transmissibility, incidence rate, and the number of reported cases of COVID-19, we collected panel data and used generalized estimating equations. We also explored whether there is a lag effect and the different times of meteorological factors on the three outcome variables. Results Precipitation and wind speed had a negative effect on transmissibility, incidence rate, and the number of reported cases, while humidity had a positive effect on them. The higher the temperature, the lower the transmissibility. The temperature had a lag effect on the incidence rate, while the remaining five meteorological factors had immediate and lag effects on the incidence rate and the number of reported cases. Conclusion Meteorological factors had similar effects on incidence rate and number of reported cases, but different effects on transmissibility. Temperature, relative humidity, precipitation, sunshine hours, and wind speed had immediate and lag effects on transmissibility, but with different lag times. An increase in temperature may first cause a decrease in virus transmissibility and then lead to a decrease in incidence rate. Also, the mechanism of the role of meteorological factors in the process of transmissibility to incidence rate needs to be further explored.

Epidemiological Characteristics and Transmissibility of Human Immunodeficiency Virus in Nanning City, China, 2001-2020.

Background: Human immunodeficiency virus (HIV) is a single-stranded RNA virus that can weaken the body's cellular and humoral immunity and is a serious disease without specific drug management and vaccine. This study aimed to evaluate the epidemiologic characteristics and transmissibility of HIV. Methods: Data on HIV follow-up were collected in Nanning City, Guangxi Zhuang Autonomous, China. An HIV transmission dynamics model was built to simulate the transmission of HIV and estimate its transmissibility by comparing the effective reproduction number (Reff ) at different stages: the rapid growth period from January 2001 to March 2005, slow growth period from April 2005 to April 2011, and the plateau from May 2011 to December 2019 of HIV in Nanning City. Results: High-risk areas of HIV prevalence in Nanning City were mainly concentrated in suburbs. Furthermore, high-risk groups were those of older age, with lower income, and lower education levels. The Reff in each stage (rapid growth, slow growth, and plateau) were 2.74, 1.62, and 1.15, respectively, which suggests the transmissibility of HIV in Nanning City has declined and prevention and control measures have achieved significant results. Conclusion: Over the past 20 years, the HIV incidence in Nanning has remained at a relatively high level, but its development trend has been curbed. Transmissibility was reduced from 2.74 to 1.15. Therefore, the prevention and treatment measures in Nanning City have achieved significant improvement.

An Easy-to-Use Public Health-Driven Method (the Generalized Logistic Differential Equation Model) Accurately Simulated COVID-19 Epidemic in Wuhan and Correctly Determined the Early Warning Time

Introduction Modeling on infectious diseases is significant to facilitate public health policymaking. There are two main mathematical methods that can be used for the simulation of the epidemic and prediction of optimal early warning timing: the logistic differential equation (LDE) model and the more complex generalized logistic differential equation (GLDE) model. This study aimed to compare and analyze these two models. Methods We collected data on (coronavirus disease 2019) COVID-19 and four other infectious diseases and classified the data into four categories: different transmission routes, different epidemic intensities, different time scales, and different regions, using R2 to compare and analyze the goodness-of-fit of LDE and GLDE models. Results Both models fitted the epidemic curves well, and all results were statistically significant. The R2 test value of COVID-19 was 0.924 (p < 0.001) fitted by the GLDE model and 0.916 (p < 0.001) fitted by the LDE model. The R2 test value varied between 0.793 and 0.966 fitted by the GLDE model and varied between 0.594 and 0.922 fitted by the LDE model for diseases with different transmission routes. The R2 test values varied between 0.853 and 0.939 fitted by the GLDE model and varied from 0.687 to 0.769 fitted by the LDE model for diseases with different prevalence intensities. The R2 test value varied between 0.706 and 0.917 fitted by the GLDE model and varied between 0.410 and 0.898 fitted by the LDE model for diseases with different time scales. The GLDE model also performed better with nation-level data with the R2 test values between 0.897 and 0.970 vs. 0.731 and 0.953 that fitted by the LDE model. Both models could characterize the patterns of the epidemics well and calculate the acceleration weeks. Conclusion The GLDE model provides more accurate goodness-of-fit to the data than the LDE model. The GLDE model is able to handle asymmetric data by introducing shape parameters that allow it to fit data with various distributions. The LDE model provides an earlier epidemic acceleration week than the GLDE model. We conclude that the GLDE model is more advantageous in asymmetric infectious disease data simulation.

The optimal vaccination strategy to control COVID-19: a modeling study in Wuhan City, China.

BACKGROUND: Reaching optimal vaccination rates is an essential public health strategy to control the coronavirus disease 2019 (COVID-19) pandemic. This study aimed to simulate the optimal vaccination strategy to control the disease by developing an age-specific model based on the current transmission patterns of COVID-19 in Wuhan City, China. METHODS: We collected two indicators of COVID-19, including illness onset data and age of confirmed case in Wuhan City, from December 2, 2019, to March 16, 2020. The reported cases were divided into four age groups: group 1, ≤ 14 years old; group 2, 15 to 44 years old; group 3, 44 to 64 years old; and group 4, ≥ 65 years old. An age-specific susceptible-exposed-symptomatic-asymptomatic-recovered/removed model was developed to estimate the transmissibility and simulate the optimal vaccination strategy. The effective reproduction number (Reff) was used to estimate the transmission interaction in different age groups. RESULTS: A total of 47 722 new cases were reported in Wuhan City from December 2, 2019, to March 16, 2020. Before the travel ban of Wuhan City, the highest transmissibility was observed among age group 2 (Reff = 4.28), followed by group 2 to 3 (Reff = 2.61), and group 2 to 4 (Reff = 1.69). China should vaccinate at least 85% of the total population to interrupt transmission. The priority for controlling transmission should be to vaccinate 5% to 8% of individuals in age group 2 per day (ultimately vaccinated 90% of age group 2), followed by 10% of age group 3 per day (ultimately vaccinated 90% age group 3). However, the optimal vaccination strategy for reducing the disease severity identified individuals ≥ 65 years old as a priority group, followed by those 45-64 years old. CONCLUSIONS: Approximately 85% of the total population (nearly 1.2 billion people) should be vaccinated to build an immune barrier in China to safely consider removing border restrictions. Based on these results, we concluded that 90% of adults aged 15-64 years should first be vaccinated to prevent transmission in China.

Appropriate Strategies for Reducing the Negative Impact of Online Reports of Suicide and Public Opinion From Social Media in China.

Suicide events may have a negative impact on all of society. The media plays a significant role in suicide prevention. Therefore, the aims of this study are (a) to understand the association between characteristics of suicide events and characteristics of who committed suicide, and event impact indexes (EIIs) of suicide reported on the internet; (b) to analyze violation of recommendations for reporting suicide by Weibo, and (c) to investigate the effect of online reports of suicide on public opinion. We carried out a content analysis of online reports of suicide. This study analyzed 113 suicide events, 300 news reports of suicide, and 2,654 Weibo comments about suicide collected from the WeiboReach between 2015 and 2020. We used a t-test and analysis of variance (ANOVA) to explore the potential factors associated with the EIIs of suicide events. The results found that (a) The suicide events reported on the internet during COVID-19 and those related to celebrities and students tend to have higher EIIs; (b) suicide reports on Weibo frequently violated WHO recommendations for suicide reporting in the media; and (c) public opinion of suicide reporting in the online media was mostly emotional and irrational, which is not beneficial for public mental health and suicide prevention. In conclusion, first, the situation of many people working from home or studying from home and spreading more time online during COVID-19 may lead to suicide events obtain more public attention. Online media could further improve public responsible reporting and daily media-content surveillance, especially taking particular care in those suicide events during COVID-19, and related to celebrities and students, which may have a higher event impact on the internet. Second, health managers should regular assessment of observance of the WHO recommendations for suicide reporting by online social media to prevent suicide. Third, health communication managers should use big data to identify, assess, and manage harmful information about suicide; and track anyone affected by suicide-related reports on social media to reduce the negative impact of public opinion to intervene suicide in the early stage of suicide.

Capturing the Trajectory of Psychological Status and Analyzing Online Public Reactions During the Coronavirus Disease 2019 Pandemic Through Weibo Posts in China.

When a major, sudden infectious disease occurs, people tend to react emotionally and display reactions such as tension, anxiety, fear, depression, and somatization symptoms. Social media played a substantial awareness role in developing countries during the outbreak of coronavirus disease 2019 (COVID-19). This study aimed to analyze public opinion regarding COVID-19 and to explore the trajectory of psychological status and online public reactions to the COVID-19 pandemic by examining online content from Weibo in China. This study consisted of three steps: first, Weibo posts created during the pandemic were collected and preprocessed on a large scale; second, public sentiment orientation was classified as "optimistic/pessimistic/neutral" orientation via natural language processing and manual determination procedures; and third, qualitative and quantitative analyses were conducted to reveal the trajectory of public psychological status and online public reactions during the COVID-19 pandemic. Public psychological status differed in different periods of the pandemic (from December 2019 to May 2020). The newly confirmed cases had an almost 1-month lagged effect on public psychological status. Among the 15 events with high impact indexes or related to government decisions, there were 10 optimism orientation > pessimism orientation (OP) events (2/3) and 5 pessimism orientation > optimism orientation (PO) events (1/3). Among the top two OP events, the high-frequency words were "race against time" and "support," while in the top two PO events, the high-frequency words were "irrationally purchase" and "pass away." We proposed a hypothesis that people developed negative self-perception when they received PO events, but their cognition was developed by how these external stimuli were processed and evaluated. These results offer implications for public health policymakers on understanding public psychological status from social media. This study demonstrates the benefits of promoting psychological healthcare and hygiene activity in the early period and improving risk perception for the public based on public opinion and the coping abilities of people. Health managers should focus on disseminating socially oriented strategies to improve the policy literacy of Internet users, thereby facilitating the disease prevention work for the COVID-19 pandemic and other major public events.

Impact of interventions on the incidence of natural focal diseases during the outbreak of COVID-19 in Jiangsu Province, China.

BACKGROUND: During the period of the coronavirus disease 2019 (COVID-19) outbreak, strong intervention measures, such as lockdown, travel restriction, and suspension of work and production, may have curbed the spread of other infectious diseases, including natural focal diseases. In this study, we aimed to study the impact of COVID-19 prevention and control measures on the reported incidence of natural focal diseases (brucellosis, malaria, hemorrhagic fever with renal syndrome [HFRS], dengue, severe fever with thrombocytopenia syndrome [SFTS], rabies, tsutsugamushi and Japanese encephalitis [JE]). METHODS: The data on daily COVID-19 confirmed cases and natural focal disease cases were collected from Jiangsu Provincial Center for Disease Control and Prevention (Jiangsu Provincial CDC). We described and compared the difference between the incidence in 2020 and the incidence in 2015-2019 in four aspects: trend in reported incidence, age, sex, and urban and rural distribution. An autoregressive integrated moving average (ARIMA) (p, d, q) × (P, D, Q)s model was adopted for natural focal diseases, malaria and severe fever with thrombocytopenia syndrome (SFTS), and an ARIMA (p, d, q) model was adopted for dengue. Nonparametric tests were used to compare the reported and the predicted incidence in 2020, the incidence in 2020 and the previous 4 years, and the difference between the duration from illness onset date to diagnosed date (DID) in 2020 and in the previous 4 years. The determination coefficient (R2) was used to evaluate the goodness of fit of the model simulation. RESULTS: Natural focal diseases in Jiangsu Province showed a long-term seasonal trend. The reported incidence of natural focal diseases, malaria and dengue in 2020 was lower than the predicted incidence, and the difference was statistically significant (P < 0.05). The reported incidence of brucellosis in July, August, October and November 2020, and SFTS in May to November 2020 was higher than that in the same period in the previous 4 years (P < 0.05). The reported incidence of malaria in April to December 2020, HFRS in March, May and December 2020, and dengue in July to November 2020 was lower than that in the same period in the previous 4 years (P < 0.05). In males, the reported incidence of malaria in 2020 was lower than that in the previous 4 years, and the reported incidence of dengue in 2020 was lower than that in 2017-2019. The reported incidence of malaria in the 20-60-year age group was lower than that in the previous 4 years; the reported incidence of dengue in the 40-60-year age group was lower than that in 2016-2018. The reported cases of malaria in both urban and rural areas were lower than in the previous 4 years. The DID of brucellosis and SFTS in 2020 was shorter than that in 2015-2018; the DID of tsutsugamushi in 2020 was shorter than that in the previous 4 years. CONCLUSIONS: Interventions for COVID-19 may help control the epidemics of natural focal diseases in Jiangsu Province. The reported incidence of natural focal diseases, especially malaria and dengue, decreased during the outbreak of COVID-19 in 2020. COVID-19 prevention and control measures had the greatest impact on the reported incidence of natural focal diseases in males and people in the 20-60-year age group.

Containing the Transmission of COVID-19: A Modeling Study in 160 Countries.

Background: It is much valuable to evaluate the comparative effectiveness of the coronavirus disease 2019 (COVID-19) prevention and control in the non-pharmacological intervention phase of the pandemic across countries and identify useful experiences that could be generalized worldwide. Methods: In this study, we developed a susceptible-exposure-infectious-asymptomatic-removed (SEIAR) model to fit the daily reported COVID-19 cases in 160 countries. The time-varying reproduction number (R t ) that was estimated through fitting the mathematical model was adopted to quantify the transmissibility. We defined a synthetic index (I AC ) based on the value of R t to reflect the national capability to control COVID-19. Results: The goodness-of-fit tests showed that the SEIAR model fitted the data of the 160 countries well. At the beginning of the epidemic, the values of R t of countries in the European region were generally higher than those in other regions. Among the 160 countries included in the study, all European countries had the ability to control the COVID-19 epidemic. The Western Pacific Region did best in continuous control of the epidemic, with a total of 73.76% of countries that can continuously control the COVID-19 epidemic, while only 43.63% of the countries in the European Region continuously controlled the epidemic, followed by the Region of Americas with 52.53% of countries, the Southeast Asian Region with 48% of countries, the African Region with 46.81% of countries, and the Eastern Mediterranean Region with 40.48% of countries. Conclusion: Large variations in controlling the COVID-19 epidemic existed across countries. The world could benefit from the experience of some countries that demonstrated the highest containment capabilities.

Control measures during the COVID-19 outbreak reduced the transmission of hand, foot, and mouth disease

Control measures during the coronavirus disease 2019 (COVID-19) outbreak may have limited the spread of infectious diseases. This study aimed to analyse the impact of COVID-19 on the spread of hand, foot, and mouth disease (HFMD) in China. A mathematical model was established to fit the reported data of HFMD in six selected cities in mainland China from 2015 to 2020. The absolute difference (AD) and relative difference (RD) between the reported incidence in 2020, and simulated maximum, minimum, or median incidence of HFMD in 2015-2019 were calculated. The incidence and Reff of HFMD have decreased in six selected cities since the outbreak of COVID-19, and in the second half of 2020, the incidence and Reff of HFMD have rebounded. The results show that the total attack rate (TAR) in 2020 was lower than the maximum, minimum, and median TAR fitted in previous years in six selected cities (except Changsha city). For the maximum, median, minimum fitted TAR, the range of RD (%) is 42•20-99•20%, 36•35-98•41% 48•35-96•23% (except Changsha city) respectively. The preventive and control measures of COVID-19 have significantly contributed to the containment of HFMD transmission.

Effectiveness of potential antiviral treatments in COVID-19 transmission control: a modelling study.

BACKGROUND: Novel coronavirus disease 2019 (COVID-19) causes an immense disease burden. Although public health countermeasures effectively controlled the epidemic in China, non-pharmaceutical interventions can neither be maintained indefinitely nor conveniently implemented globally. Vaccination is mainly used to prevent COVID-19, and most current antiviral treatment evaluations focus on clinical efficacy. Therefore, we conducted population-based simulations to assess antiviral treatment effectiveness among different age groups based on its clinical efficacy. METHODS: We collected COVID-19 data of Wuhan City from published literature and established a database (from 2 December 2019 to 16 March 2020). We developed an age-specific model to evaluate the effectiveness of antiviral treatment in patients with COVID-19. Efficacy was divided into three types: (1) viral activity reduction, reflected as transmission rate decrease [reduction was set as v (0-0.8) to simulate hypothetical antiviral treatments]; (2) reduction in the duration time from symptom onset to patient recovery/removal, reflected as a 1/γ decrease (reduction was set as 1-3 days to simulate hypothetical or real-life antiviral treatments, and the time of asymptomatic was reduced by the same proportion); (3) fatality rate reduction in severely ill patients (fc) [reduction (z) was set as 0.3 to simulate real-life antiviral treatments]. The population was divided into four age groups (groups 1, 2, 3 and 4), which included those aged ≤ 14; 15-44; 45-64; and ≥ 65 years, respectively. Evaluation indices were based on outbreak duration, cumulative number of cases, total attack rate (TAR), peak date, number of peak cases, and case fatality rate (f). RESULTS: Comparing the simulation results of combination and single medication therapy s, all four age groups showed better results with combination medication. When 1/γ = 2 and v = 0.4, age group 2 had the highest TAR reduction rate (98.48%, 56.01-0.85%). When 1/γ = 2, z = 0.3, and v = 0.1, age group 1 had the highest reduction rate of f (83.08%, 0.71-0.12%). CONCLUSIONS: Antiviral treatments are more effective in COVID-19 transmission control than in mortality reduction. Overall, antiviral treatments were more effective in younger age groups, while older age groups showed higher COVID-19 prevalence and mortality. Therefore, physicians should pay more attention to prevention of viral spread and patients deaths when providing antiviral treatments to patients of older age groups.