Mathematical model of transmission dynamics and optimal control strategies for 2009 A/H1N1 influenza in the Republic of Korea

Time scale theory on stability of explicit and implicit discrete epidemic models: applications to Swine flu outbreak

Time scales theory has been in use since the 1980s with many applications. Only very recently, it has been used to describe within-host and between-hosts dynamics of infectious diseases. In this study, we present explicit and implicit discrete epidemic models motivated by the time scales modeling approach. We use these models to formulate the basic reproduction number, which determines whether an outbreak occurs or the disease dies out. We discuss the stability of the disease-free and endemic equilibrium points using the linearization method and Lyapunov function. Furthermore, we apply our models to swine flu outbreak data to demonstrate that the discrete models can accurately describe the epidemic dynamics. Our comparison analysis shows that the implicit discrete model can best describe the data regardless of the data frequency. In addition, we perform the sensitivity analysis on the key parameters of the models to study how these parameters impact the basic reproduction number.

Final epidemic size and optimal control of socio-economic multi-group influenza model

Flu, a common respiratory disease is caused mainly by the influenza virus. The Avian influenza (H5N1) outbreaks, as well as the 2009 H1N1 pandemic, have heightened global concerns about the emergence of a lethal influenza virus capable of causing a catastrophic pandemic. During the early stages of an epidemic a favourable change in the behaviour of people can be of utmost importance. An economic status-based (higher and lower economic class) structured model is formulated to examine the behavioural effect in controlling influenza. Following that, we have introduced controls into the model to analyse the efficacy of antiviral treatment in restraining infections in both economic classes and examined an optimal control problem. We have obtained the reproduction number R 0 along with the final epidemic size for both the strata and the relation between reproduction number and epidemic size. Through numerical simulation and global sensitivity analysis, we have shown the importance of the parameters ϕ i , ϕ s , η 2 , β and θ on reproduction number. Our result shows that by increasing ϕ 1 , η 2 and by decreasing β , θ and ϕ s , we can reduce the infection in both the economic group. As a result of our analysis, we have found that the reduction of infections and their level of adversity is directly influenced by positive behavioural patterns or changes as without control susceptible population is increased by 23 % , the infective population is decreased by 48.54 % and the recovered population is increased by 23.23 % in the higher economic group who opted changed behaviour as compared to the lower the economic group (people living with normal behaviour). Thus normal behaviour contributes to the spread and growth of viruses and adds to the hassle. We also examined how antiviral drug control impacts both economic strata and found that in the higher economic strata, the susceptible population increased by 53.84 % , the infective population decreased by 33.6 % and the recovered population improved by 62.29 % as compared to the lower economic group, the susceptible population has increased by 19.04 % , the infective population is decreased by 17.29 % and the recovered population is improved by 47.82 % . Our results enlighten the role that how different behaviour in separate socio-economic class plays an important role in changing the dynamics of the system and also affects the basic reproduction number. The results of our study suggest that it is important to adopt a modified behaviour like social distancing, wearing masks accompanying the time-dependent controls in the form of an antiviral drug's effectiveness to combat infections and increasing the proportion of the susceptible population.

A discrete model for the evaluation of public policies: The case of Colombia during the COVID-19 pandemic

In mathematical epidemiology, it is usual to implement compartmental models to study the transmission of diseases, allowing comprehension of the outbreak dynamics. Thus, it is necessary to identify the natural history of the disease and to establish promissory relations between the structure of a mathematical model, as well as its parameters, with control-related strategies (real interventions) and relevant socio-cultural behaviors. However, we identified gaps between the model creation and its implementation for the use of decision-makers for policy design. We aim to cover these gaps by proposing a discrete mathematical model with parameters having intuitive meaning to be implemented to help decision-makers in control policy design. The model considers novel contagion probabilities, quarantine, and diffusion processes to represent the recovery and mortality dynamics. We applied mathematical model for COVID-19 to Colombia and some of its localities; moreover, the model structure could be adapted for other diseases. Subsequently, we implemented it on a web platform (MathCOVID) for the usage of decision-makers to simulate the effect of policies such as lock-downs, social distancing, identification in the contagion network, and connectivity among populations. Furthermore, it was possible to assess the effects of migration and vaccination strategies as time-dependent inputs. Finally, the platform was capable of simulating the effects of applying one or more policies simultaneously.

Propagation of H1N1 virus through saliva movement in oesophagus: a mathematical model

H1N1 (Swine flu) is caused by the influenza A virus which belongs to the Orthomyxoviridae family. Influenza A is very harmful to the elderly, and people with chronic respiratory disease and cardiovascular disease. Therefore, it is essential to analyse the behaviour of virus transmission through the saliva movement in oesophagus. A mathematical paradigm is developed to study the saliva movement under the applications of transverse magnetic field. Jeffrey fluid model is considered for saliva to show the viscoelastic nature. The flow nature is considered creeping and assumptions of long wavelength and low Reynolds number are adopted for analytical solutions. The Basset-Boussinesq-Oseen equation is employed to understand the propagation of H1N1 virus through saliva under the effect of applicable forces such as gravity, virtual mass, basset force, and drag forces. The suitable data for saliva, oesophagus and H1N1 virus are taken from the existing literature for simulation of the results using MATLAB software. From the graphical results, it is observed that the susceptibility to viral infections is less because the magnetic field reduces the motion of the virus particle. Further, the chances of infections in males are more as compared to females and children due to variation in viscosity of saliva. Such findings provide an understanding of the mechanics of the virus floating through the saliva (viscoelastic fluids) in the oesophagus.

Incorporating global dynamics to improve the accuracy of disease models: Example of a COVID-19 SIR model

Mathematical models of infectious diseases exhibit robust dynamics, such as stable endemic, disease-free equilibriums or convergence of the solutions to periodic epidemic waves. The present work shows that the accuracy of such dynamics can be significantly improved by including global effects of host movements in disease models. To demonstrate improved accuracy, we extended a standard Susceptible-Infected-Recovered (SIR) model by incorporating the global dynamics of the COVID-19 pandemic. The extended SIR model assumes three possibilities for susceptible individuals traveling outside of their community:

• They can return to the community without any exposure to the infection.

• They can be exposed and develop symptoms after returning to the community.

• They can be tested positively during the trip and remain quarantined until fully recovered.

To examine the predictive accuracy of the extended SIR model, we studied the prevalence of the COVID-19 infection in six randomly selected cities and states in the United States: Kansas City, Saint Louis, San Francisco, Missouri, Illinois, and Arizona. The extended SIR model was parameterized using a two-step model-fitting algorithm. The extended SIR model significantly outperformed the standard SIR model and revealed oscillatory behaviors with an increasing trend of infected individuals. In conclusion, the analytics and predictive accuracy of disease models can be significantly improved by incorporating the global dynamics of the infection.

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.

Current forecast of COVID-19 in Mexico: A Bayesian and machine learning approaches

The COVID-19 pandemic has been widely spread and affected millions of people and caused hundreds of deaths worldwide, especially in patients with comorbilities and COVID-19. This manuscript aims to present models to predict, firstly, the number of coronavirus cases and secondly, the hospital care demand and mortality based on COVID-19 patients who have been diagnosed with other diseases. For the first part, I present a projection of the spread of coronavirus in Mexico, which is based on a contact tracing model using Bayesian inference. I investigate the health profile of individuals diagnosed with coronavirus to predict their type of patient care (inpatient or outpatient) and survival. Specifically, I analyze the comorbidity associated with coronavirus using Machine Learning. I have implemented two classifiers: I use the first classifier to predict the type of care procedure that a person diagnosed with coronavirus presenting chronic diseases will obtain (i.e. outpatient or hospitalised), in this way I estimate the hospital care demand; I use the second classifier to predict the survival or mortality of the patient (i.e. survived or deceased). I present two techniques to deal with these kinds of unbalanced datasets related to outpatient/hospitalised and survived/deceased cases (which occur in general for these types of coronavirus datasets) to obtain a better performance for the classification.

Optimal control of pattern formations for an SIR reaction-diffusion epidemic model

Patterns arising from the reaction-diffusion epidemic model provide insightful aspects into the transmission of infectious diseases. For a classic SIR reaction-diffusion epidemic model, we review its Turing pattern formations with different transmission rates. A quantitative indicator, "normal serious prevalent area (NSPA)", is introduced to characterize the relationship between patterns and the extent of the epidemic. The extent of epidemic is positively correlated to NSPA. To effectively reduce NSPA of patterns under the large transmission rates, taken removed (recovery or isolation) rate as a control parameter, we consider the mathematical formulation and numerical solution of an optimal control problem for the SIR reaction-diffusion model. Numerical experiments demonstrate the effectiveness of our method in terms of control effect, control precision and control cost.

Six Cs of pandemic emergency management: A case study of Taiwan's initial response to the COVID-19 pandemic

A review of the disaster literature indicates that emergency responses to pandemics are often understudied; the current COVID-19 crisis provides an important opportunity to improve awareness and understanding about this and other contagious and disruptive diseases. With this in mind, this study examines Taiwan's response to COVID-19 because it was successful in spite of a high probability of contagion. The paper first explores the assertion that cognition, communication, collaboration, and control are vital for effective disaster response; it then indicates the need to consider two additional Cs: confidence (trust of government's competency) and coproduction (public participation in disaster transmission prevention). The paper also conducts a qualitative descriptive study of the Taiwan government's response timeline with examples of each of these concepts in action. To further illustrate the need for the two additional Cs, survey data illustrate how public confidence serves as a pivot between government's COVID-19 response and citizen coproduction in COVID-19 transmission prevention.

Dynamic analysis of a SIQR epidemic model considering the interaction of environmental differences

Infectious diseases have a devastating impact on individual health and social development. Different external environmental factors will affect the scale and the speed of disease outbreaks, such as sanitary conditions and policy interventions. In this paper, we attempt to establish a dual-system susceptible-infectious-quarantine-recovered model with different environmental impacts to explore it. For the deterministic model, we calculate the basic reproduction number, simultaneously, and investigate the local asymptotic stability of the disease-free equilibrium and the endemic equilibrium. Numerical simulations and theoretical analyses verify the conclusion of this paper. It is a surprise that there is a great probability of finding a quarantine inflection point, which can effectively control the scale of infection outbreak when two different systems of infection rate and recovery rate are determined.

Advancing sustainable development goals through immunization: a literature review

BACKGROUND

Immunization directly impacts health (SDG3) and brings a contribution to 14 out of the 17 Sustainable Development Goals (SDGs), such as ending poverty, reducing hunger, and reducing inequalities. Therefore, immunization is recognized to play a central role in reaching the SDGs, especially in low- and middle-income countries (LMICs). Despite continuous interventions to strengthen immunization systems and to adequately respond to emergency immunization during epidemics, the immunization-related indicators for SDG3 lag behind in sub-Saharan Africa. Especially taking into account the current Covid19 pandemic, the current performance on the connected SDGs is both a cause and a result of this.

METHODS

We conduct a literature review through a keyword search strategy complemented with handpicking and snowballing from earlier reviews. After title and abstract screening, we conducted a qualitative analysis of key insights and categorized them according to showing the impact of immunization on SDGs, sustainability challenges, and model-based solutions to these challenges.

RESULTS

We reveal the leveraging mechanisms triggered by immunization and position them vis-à-vis the SDGs, within the framework of Public Health and Planetary Health. Several challenges for sustainable control of vaccine-preventable diseases are identified: access to immunization services, global vaccine availability to LMICs, context-dependent vaccine effectiveness, safe and affordable vaccines, local/regional vaccine production, public-private partnerships, and immunization capacity/capability building. Model-based approaches that support SDG-promoting interventions concerning immunization systems are analyzed in light of the strategic priorities of the Immunization Agenda 2030.

CONCLUSIONS

In general terms, it can be concluded that relevant future research requires (i) design for system resilience, (ii) transdisciplinary modeling, (iii) connecting interventions in immunization with SDG outcomes, (iv) designing interventions and their implementation simultaneously, (v) offering tailored solutions, and (vi) model coordination and integration of services and partnerships. The research and health community is called upon to join forces to activate existing knowledge, generate new insights and develop decision-supporting tools for Low-and Middle-Income Countries' health authorities and communities to leverage immunization in its transformational role toward successfully meeting the SDGs in 2030.

Modeling the Spread and Control of COVID-19

Data-centric models of COVID-19 have been attempted, but have certain limitations. In this work, we propose an agent-based model of the epidemic in a confined space of agents representing humans. An extension to the SEIR model allows us to consider the difference between the appearance (black-box view) of the spread of disease and the real situation (glass-box view). Our model allows for simulations of lockdowns, social distancing, personal hygiene, quarantine, and hospitalization, with further considerations of different parameters, such as the extent to which hygiene and social distancing are observed in a population. Our results provide qualitative indications of the effects of various policies and parameters, for instance, that lockdowns by themselves are extremely unlikely to bring an end to an epidemic and may indeed make things worse, that social distancing is more important than personal hygiene, and that the growth of infection is significantly reduced for moderately high levels of social distancing and hygiene, even in the absence of herd immunity.

Changing readiness to mitigate SARS-CoV-2 steered long-term epidemic and social trajectories

Societal responses crucially shape the course of a pandemic, but are difficult to predict. Mitigation measures such as social distancing are here assumed to minimize a utility function that consists of two conflicting sub-targets, the disease related mortality and the multifaceted consequences of mitigation. The relative weight of the two sub-targets defines the mitigation readiness H, which entails the political, social, and psychological aspects of decision making. The dynamics of social and behavioral mitigation thus follows an adaptive rule, which in turn is mediated by a non-adaptive dynamics of H. This framework for social dynamics is integrated into an epidemiological model and applied to the ongoing SARS-CoV-2 pandemic. Unperturbed simulations accurately reproduce diverse epidemic and mitigation trajectories from 2020 to 2021, reported from 11 European countries, Iran, and 8 US states. High regional variability in the severity and duration of the spring lockdown and in peak mortality rates of the first SARS-CoV-2 wave can be explained by differences in the reconstructed readiness H. A ubiquitous temporal decrease of H has greatly intensified second and third waves and slowed down their decay. The unprecedented skill of the model suggests that the combination of an adaptive and a non-adaptive rule may constitute a more fundamental mode in social dynamics. Its implementation in an epidemic context can produce realistic long-term scenarios relevant for strategic planning, such as on the feasibility of a zero-infection target or on the evolutionary arms race between mutations of SARS-CoV-2 and social responses.

Nonlinear Dynamics of the Introduction of a New SARS-CoV-2 Variant with Different Infectiousness

Several variants of the SARS-CoV-2 virus have been detected during the COVID-19 pandemic. Some of these new variants have been of health public concern due to their higher infectiousness. We propose a theoretical mathematical model based on differential equations to study the effect of introducing a new, more transmissible SARS-CoV-2 variant in a population. The mathematical model is formulated in such a way that it takes into account the higher transmission rate of the new SARS-CoV-2 strain and the subpopulation of asymptomatic carriers. We find the basic reproduction number R0 using the method of the next generation matrix. This threshold parameter is crucial since it indicates what parameters play an important role in the outcome of the COVID-19 pandemic. We study the local stability of the infection-free and endemic equilibrium states, which are potential outcomes of a pandemic. Moreover, by using a suitable Lyapunov functional and the LaSalle invariant principle, it is proved that if the basic reproduction number is less than unity, the infection-free equilibrium is globally asymptotically stable. Our study shows that the new more transmissible SARS-CoV-2 variant will prevail and the prevalence of the preexistent variant would decrease and eventually disappear. We perform numerical simulations to support the analytic results and to show some effects of a new more transmissible SARS-CoV-2 variant in a population.

DYNAMICS OF AN INFECTIOUS DISEASE IN THE PRESENCE OF SATURATED MEDICAL TREATMENT OF HOLLING TYPE III AND SELF-PROTECTION

A nonlinear SEIR model is formulated and analyzed. This model accounts for three important interventions — the saturated treatment on infective individuals, the screening on the exposed individuals and the information induced self-protection on susceptible individuals. Existence and stability of equilibria are discussed. A sensitivity analysis for the model parameters is performed and we identified the parameters which are more sensitive to the model system. The sensitivity analysis is further followed up with the two parameters heat plot that determines the regions for the parametric values in which the system is either stable or unstable. Further, an optimal control problem is formulated by considering screening and treatment as control variables and corresponding cost functional is constructed. Using Pontryagin’s Maximum Principle, paths of optimal controls are obtained analytically. A comparative study is conducted numerically to explore and analyze analytical results. We note that in absence of treatment, screening policy may be a cost-effective choice to keep a tab on the disease. However, comprehensive effect of both screening and treatment has a huge impact, which is highly effective and least expensive. It is also noted that treatment is effective for mild epidemic whereas screening has a significant effect on the disease burden while epidemic is severe. For a range of basic reproduction number, effect of self-protection and saturation in treatment is also explored numerically.

Impact of a New SARS-CoV-2 Variant on the Population: A Mathematical Modeling Approach

Several SARS-CoV-2 variants have emerged around the world, and the appearance of other variants depends on many factors. These new variants might have different characteristics that can affect the transmissibility and death rate. The administration of vaccines against the coronavirus disease 2019 (COVID-19) started in early December of 2020 and in some countries the vaccines will not soon be widely available. For this article, we studied the impact of a new more transmissible SARS-CoV-2 strain on prevalence, hospitalizations, and deaths related to the SARS-CoV-2 virus. We studied different scenarios regarding the transmissibility in order to provide a scientific support for public health policies and bring awareness of potential future situations related to the COVID-19 pandemic. We constructed a compartmental mathematical model based on differential equations to study these different scenarios. In this way, we are able to understand how a new, more infectious strain of the virus can impact the dynamics of the COVID-19 pandemic. We studied several metrics related to the possible outcomes of the COVID-19 pandemic in order to assess the impact of a higher transmissibility of a new SARS-CoV-2 strain on these metrics. We found that, even if the new variant has the same death rate, its high transmissibility can increase the number of infected people, those hospitalized, and deaths. The simulation results show that health institutions need to focus on increasing non-pharmaceutical interventions and the pace of vaccine inoculation since a new variant with higher transmissibility, such as, for example, VOC-202012/01 of lineage B.1.1.7, may cause more devastating outcomes in the population.

New global dynamical results and application of several SVEIS epidemic models with temporary immunity

This work applies a novel geometric criterion for global stability of nonlinear autonomous differential equations generalized by Lu and Lu (2017) to establish global threshold dynamics for several SVEIS epidemic models with temporary immunity, incorporating saturated incidence and nonmonotone incidence with psychological effect, and an SVEIS model with saturated incidence and partial temporary immunity. Incidentally, global stability for the SVEIS models with saturated incidence in Cai and Li (2009), Sahu and Dhar (2012) is completely solved. Furthermore, employing the DEDiscover simulation tool, the parameters in Sahu and Dhar'model are estimated with the 2009-2010 pandemic H1N1 case data in Hong Kong China, and it is validated that the vaccination programme indeed avoided subsequent potential outbreak waves of the pandemic. Finally, global sensitivity analysis reveals that multiple control measures should be utilized jointly to cut down the peak of the waves dramatically and delay the arrival of the second wave, thereinto timely vaccination is particularly effective.

Qualitative analysis of a mathematical model with presymptomatic individuals and two SARS-CoV-2 variants

The SARS-CoV-2 continues to spread across the world. During this COVID-19 pandemic, several variants of the SARS-CoV-2 have been found. Some of these new variants like the VOC-202012/01 of lineage B.1.1.7 or the most recently B.1.617 emerging in India have a higher infectiousness than those previously prevalent. We propose a mathematical model based on ordinary differential equations to investigate potential consequences of the appearance of a new more transmissible SARS-CoV-2 strain in a given region. The proposed mathematical model incorporates the presymptomatic and asymptomatic subpopulations in addition to the more usual susceptible, exposed, infected, and recovered subpopulations. This is important from a realistic point of view since it has been found recently that presymptomatic and asymptomatic individuals are relevant spreaders of the SARS-CoV-2. Using the next-generation matrix method, we find the basic reproduction number, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {R}}_{0}$$\end{document}R0, an important threshold parameter that provides insight regarding the evolution and outcome of a certain instance of the COVID-19 pandemic. The local and global stability of system equilibria are also presented. In particular, for the global stability we construct a Lyapunov functional and use the LaSalle invariant principle to prove that if the basic reproduction ratio is less than unity, the infection-free equilibrium is globally asymptotically stable. On the other hand, if \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {R}}_{0}>1$$\end{document}R0>1 the endemic equilibrium is globally asymptotically stable. Finally, we present numerical simulations to numerically support the analytic results and to show the impact of the introduction of a new more contagious SARS-CoV-2 variant in a population.

Analysis of COVID-19 Prevention and Control Effects Based on the SEITRD Dynamic Model and Wuhan Epidemic Statistics

Since December 2019, millions of people worldwide have been diagnosed with COVID-19, which has caused enormous losses. Given that there are currently no effective treatment or prevention drugs, most countries and regions mainly rely on quarantine and travel restrictions to prevent the spread of the epidemic. How to find proper prevention and treatment methods has been a hot topic of discussion. The key to the problem is to understand when these intervention measures are the best strategies for disease control and how they might affect disease dynamics. In this paper, we build a transmission dynamic model in combination with the transmission characteristics of COVID-19. We thoroughly study the dynamical behavior of the model and analyze how to determine the relevant parameters, and how the parameters influence the transmission process. Furthermore, we subsequently compare the impact of different control strategies on the epidemic, the variables include intervention time, control duration, control intensity, and other model parameters. Finally, we can find a better control method by comparing the results under different schemes and choose the proper preventive control strategy according to the actual epidemic stage and control objectives.

A two-thresholds policy for a Filippov model in combating influenza

This work designs a two-thresholds policy for a Filippov model in combating influenza, so as to estimate when and whether to take control strategies, including the media coverage, antiviral treatment of infected individuals and vaccination of susceptible population. By introducing two tolerance thresholds [Formula: see text] and [Formula: see text] of susceptible and infected individuals, the two-thresholds policy is designed as: a vaccination program is implemented when the number of susceptible individuals is above [Formula: see text]; an antiviral treatment strategy is taken and the mass media begins to report information about influenza when the infection number is larger than [Formula: see text]; no control strategies are required in other cases. Furthermore, the global dynamics of the model are analyzed by varying these two thresholds, including the existence and dynamics of sliding mode, and the existence and global stability of equilibrium. It is shown that the model solutions ultimately converge to a pseudoequilibrium or a pseudoattractor on the switching surface, or a real equilibrium. The obtained results indicate that, by choosing susceptible and infected thresholds properly, the infection number can be remained below or at an acceptable level.

A simple model for COVID-19

An S L 1 L 2 I 1 I 2 A 1 A 2 R epidemic model is formulated that describes the spread of an epidemic in a population. The model incorporates an Erlang distribution of times of sojourn in incubating, symptomatically and asymptomatically infectious compartments. Basic properties of the model are explored, with focus on properties important in the context of current COVID-19 pandemic.

School Opening Delay Effect on Transmission Dynamics of Coronavirus Disease 2019 in Korea: Based on Mathematical Modeling and Simulation Study

BACKGROUND

Nonpharmaceutical intervention strategy is significantly important to mitigate the coronavirus disease 2019 (COVID-19) spread. One of the interventions implemented by the government is a school closure. The Ministry of Education decided to postpone the school opening from March 2 to April 6 to minimize epidemic size. We aimed to quantify the school closure effect on the COVID-19 epidemic.

METHODS

The potential effects of school opening were measured using a mathematical model considering two age groups: children (aged 19 years and younger) and adults (aged over 19). Based on susceptible-exposed-infectious-recovered model, isolation and behavior-changed susceptible individuals are additionally considered. The transmission parameters were estimated from the laboratory confirmed data reported by the Korea Centers for Disease Control and Prevention from February 16 to March 22. The model was extended with estimated parameters and estimated the expected number of confirmed cases as the transmission rate increased after school opening.

RESULTS

Assuming the transmission rate between children group would be increasing 10 fold after the schools open, approximately additional 60 cases are expected to occur from March 2 to March 9, and approximately additional 100 children cases are expected from March 9 to March 23. After March 23, the number of expected cases for children is 28.4 for 7 days and 33.6 for 14 days.

CONCLUSION

The simulation results show that the government could reduce at least 200 cases, with two announcements by the Ministry of education. After March 23, although the possibility of massive transmission in the children's age group is lower, group transmission is possible to occur.

Mathematical models of transmission dynamics and vaccine strategies in Hong Kong during the 2017-2018 winter influenza season

Two mathematical models described by simple ordinary differential equations are developed to investigate the Hong Kong influenza epidemic during 2017-2018 winter, based on overall epidemic dynamics and different influenza subtypes. The first model, describing the overall epidemic dynamics, provides the starting data for the second model which different influenza subtypes, and whose dynamics is further investigated. Weekly data from December 2017 to May 2018 are obtained from the data base of the Centre of Health Protection in Hong Kong, and used to parametrise the models. With the help of these models, we investigate the impact of different vaccination strategies and determine the corresponding critical vaccination coverage for different vaccine efficacies. The results suggest that at least 72% of Hong Kong population should have been vaccinated during 2017-2018 winter to prevent the seasonal epidemic by herd immunity (while data showed that only a maximum of 11.6% of the population were vaccinated). Our results also show that the critical vaccination coverage decreases with increasing vaccine efficacy, and the increase in one influenza subtype vaccine efficacy may lead to an increase in infections caused by a different subtype.

Estimating disease burden of a potential A(H7N9) pandemic influenza outbreak in the United States

BACKGROUND

Since spring 2013, periodic emergence of avian influenza A(H7N9) virus in China has heightened the concern for a possible pandemic outbreak among humans, though it is believed that the virus is not yet human-to-human transmittable. Till June 2017, A(H7N9) has resulted in 1533 laboratory-confirmed cases of human infections causing 592 deaths. The aim of this paper is to present disease burden estimates (measured by infection attack rates (IAR) and number of deaths) in the event of a possible pandemic outbreak caused by human-to-human transmission capability acquired by A(H7N9) virus. Even though such a pandemic will likely spread worldwide, our focus in this paper is to estimate the impact on the United States alone.

METHOD

The method first uses a data clustering technique to divide 50 states in the U.S. into a small number of clusters. Thereafter, for a few selected states in each cluster, the method employs an agent-based (AB) model to simulate human A(H7N9) influenza pandemic outbreaks. The model uses demographic and epidemiological data. A few selected non-pharmaceutical intervention (NPI) measures are applied to mitigate the outbreaks. Disease burden for the U.S. is estimated by combining results from the clusters applying a method used in stratified sampling.

RESULTS

Two possible pandemic scenarios with R 0 = 1.5 and 1.8 are examined. Infection attack rates with 95% C.I. (Confidence Interval) for R 0 = 1.5 and 1.8 are estimated to be 18.78% (17.3-20.27) and 25.05% (23.11-26.99), respectively. The corresponding number of deaths (95% C.I.), per 100,000, are 7252.3 (6598.45-7907.33) and 9670.99 (8953.66-10,389.95).

CONCLUSIONS

The results reflect a possible worst-case scenario where the outbreak extends over all states of the U.S. and antivirals and vaccines are not administered. Our disease burden estimations are also likely to be somewhat high due to the fact that only dense urban regions covering approximately 3% of the geographic area and 81% of the population are used for simulating sample outbreaks. Outcomes from these simulations are extrapolated over the remaining 19% of the population spread sparsely over 97% of the area. Furthermore, the full extent of possible NPIs, if deployed, could also have lowered the disease burden estimates.

Estimation of the Basic Reproduction Number of Novel Influenza A (H1N1) pdm09 in Elementary Schools Using the SIR Model

Background:

The novel influenza A (H1N1) pdm09 (A/H1N1pdm) pandemic of 2009-2010 had a great impact on society.

Objective:

We analyzed data from the absentee survey, conducted in elementary schools of Oita City, to evaluate the A/H1N1pdm pandemic and to estimate the basic reproductive number (R₀ ) of this novel strain.

Method:

We summarized the overall absentee data and calculated the cumulative infection rate. Then, we classified the data into 3 groups according to school size: small (<300 students), medium (300–600 students), and large (>600 students). Last, we estimated the R₀ value by using the Susceptible-Infected-Recovered (SIR) mathematical model.

Results:

Data from 60 schools and 27,403 students were analyzed. The overall cumulative infection rate was 44.4%. There were no significant differences among the grades, but the cumulative infection rate increased as the school size increased, being 37.7%, 44.4%, and 46.6% in the small, medium, and large school groups, respectively. The optimal R₀ value was 1.33, comparable with that previously reported. The data from the absentee survey were reliable, with no missing values. Hence, the R₀ derived from the SIR model closely reflected the observed R₀ . The findings support previous reports that school children are most susceptible to A/H1N1pdm virus infection and suggest that the scale of an outbreak is associated with the size of the school.

Conclusion:

Our results provide further information about the A/H1N1pdm pandemic. We propose that an absentee survey should be implemented in the early stages of an epidemic, to prevent a pandemic.