Modeling and Analysis of Infectious Disease Transmission Considering Protection and Isolation

Based on the SEIR model, two compartments for self-protection and isolation are introduced, and a more general infectious disease transmission model is proposed.Through qualitative analysis of the model, the basic reproduction number of the model is calculated, and the local asymptotic stability of the disease-free equilibrium point and the endemic equilibrium point of the model is analyzed through eigenvalue theory and Routh-Hurwitz criterion.The numerical simulation and fitting results of COVID-19 virus show that the proposed SEIQRP model can effectively describe the dynamic transmission process of the infectious disease.In the model, the three parameters, i.e.protection rate, incubation period isolation rate, and infected person isolation rate play a very critical role in the spread of the disease.Raising people's awareness of self-protection, focusing on screening for patients in the incubation period, and isolating and treating infected people can effectively reduce the spread of infectious diseases. © 2023 Northeastern University.All rights reserved.

A Mathematical Study for the Transmission of Coronavirus Disease

Globally, the COVID-19 pandemic's development has presented significant societal and economic challenges. The carriers of COVID-19 transmission have also been identified as asymptomatic infected people. Yet, most epidemic models do not consider their impact when accounting for the disease's indirect transmission. This study suggested and investigated a mathematical model replicating the spread of coronavirus disease among asymptomatic infected people. A study was conducted on every aspect of the system's solution. The equilibrium points and the basic reproduction number were computed. The endemic equilibrium point and the disease-free equilibrium point had both undergone local stability analyses. A geometric technique was used to look into the global dynamics of the endemic point, whereas the Castillo-Chavez theorem was used to look into the global stability of the disease-free point. The system's transcritical bifurcation at the disease-free point was discovered to exist. The system parameters were changed using the basic reproduction number's sensitivity technique. Ultimately, a numerical simulation was used to apply the model to the population of Iraq in order to validate the findings and define the factors that regulate illness breakout.

Differential and Time-Discrete SEIRS Models with Vaccination: Local Stability, Validation and Sensitivity Analysis Using Bulgarian COVID-19 Data

Bulgaria has the lowest COVID-19 vaccination rate in the European Union and the second-highest COVID-19 mortality rate in the world. That is why we think it is important better to understand the reason for this situation and to analyse the development of the disease over time. In this paper, an extended time-dependent SEIRS model SEIRS-VB is used to investigate the long-term behaviour of the COVID-19 epidemic. This model includes vaccination and vital dynamics. To apply the SEIRS-VB model some numerical simulation tools have been developed and for this reason a family of time-discrete variants are introduced. Suitable inverse problems for the identification of parameters in discrete models are solved. A methodology is proposed for selecting a discrete model from the constructed family, which has the closest parameter values to these in the differential SEIRS-VB model. To validate the studied models, Bulgarian COVID-19 data are used. To obtain all these results for the discrete models a mathematical analysis is carried out to illustrate some biological properties of the differential model SEIRS-VB, such as the non-negativity, boundedness, existence, and uniqueness. Using the next-generation method, the basic reproduction number associated with the model in the autonomous case is defined. The local stability of the disease-free equilibrium point is studied. Finally, a sensitivity analysis of the basic reproduction number is performed.

Mathematic Analysis of a SIHV COVID-19 Pandemic Model Taking Into Account a Vaccination Strategy

Humanity is currently living a true nightmare never seen before due to the pandemic caused by COVID-19 disease, scientific researchers are working day and night to find an ideal vaccine that eradicates this pandemic. The purpose of this paper is to investigate a SIHV pandemic model taking into account a vaccination strategy. For this aim, we consider a model with four compartments that describes the interaction between the susceptible cases S, the real infected cases I, the hospitalized, confirmed infected cases H and the vaccinated-treated individuals V. We establish the local stability of our model, depending on the basic reproduction number, by using the Routh-Hurwitz theorem. We perform some numerical simulations in order to confirm our theoretical results and discuss the effect of the rate of vaccination on controlling the spread of COVID-19. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022.

The Analysis of Dynamic Processes of Virus Transmission: How Could Diagnostic Tests and Vaccinations Can Stop COVID-19 Pandemic?

Objectives: COVID-19 reached its fourth year of pandemic since 2020. The repeated waves of infections have been driven by multiple factors such as pathological traits of variants, diagnostic accuracy, and vaccination conditions. This study revisits and analyzes the dynamic processes of viral transmission to generate new scientific knowledge. Method(s): A cascade model of viral transmission from one case to another was developed, and theoretically analyzed how the number of infected cases at time t, D+[t], can be changed at time t+1, D+[t+1], considering six parameters: 1) k:level of transmission, 2) Rt: effective reproduction number, 3) rho: capture rate of infected cases, 4) theta: immunity protection rate in individuals, 5) epsilon: evasion rate from vaccines, and 6) Sn: test sensitivity. Result(s): The formula which associates D+[t] with D+[t+1] was given as follows: D+[t+1] = K.D+[t], where K = {(1-Sn) + (1-rho) / rho}{1-Rtk (1-theta(1-epsilon))k} / {1-Rt (1-theta(1-epsilon))}. Also, assuming K be smaller than 1, the lower limit of test sensitivity to stop the viral transmission was formulated: Sn > {Rt (1-theta(1-epsilon))-Rtk(1-theta(1-epsilon))k} / {(1-Rtk(1-theta(1-epsilon))k)rho}. In example computations, the formula indicated that a one-off PCR test with the sensitivity of 85% would not be sufficient to contain highly contagious infections such as the Omicron variants, and that it would be practically impossible to control the situation with the immune-evasive sub-variants in circulation. Conclusion(s): The theory developed in this study broadens the science on evidence-based public health and will be useful for outcomes studies and informed decisions on public policy for pandemic control.Copyright © 2023

The Comparison Analysis of the Impacts of Lockdown and Quarantine Facets in the Transmission of COVID-19: Mathematical Approach

COVID-19 is the short name of the coronavirus disease discovered in Wuhan, China, in 2019. In the context of Tanzania, we develop a mathematical model in this work that compares lockdown and quarantine. Again, we provide evidence in favor of local and global stability, with the basic reproduction number, R 0 , determined to be 0.31 at the diagnostic test rates k 1 = k 2 = 0.05. In comparison to the lockdown, it has been discovered that isolating (or quarantining) affected individuals is the most effective way to stop the spread of COVID-19. Additionally, it is advised that governments in Tanzania and other African countries permit their citizens to go about their daily lives as long as they take the necessary precautions, such as donning face masks, washing their hands, and avoiding crowded gatherings in case of a recurrence of any form of COVID-19. [ FROM AUTHOR] Copyright of Computational & Mathematical Methods in Medicine is the property of Hindawi Limited and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full . (Copyright applies to all s.)

On a Novel Dynamics of a SIVR Model Using a Laplace Adomian Decomposition Based on a Vaccination Strategy

In this paper, we introduce a SIVR model using the Laplace Adomian decomposition. This model focuses on a new trend in mathematical epidemiology dedicated to studying the characteristics of vaccination of infected communities. We analyze the epidemiological parameters using equilibrium stability and numerical analysis techniques. New mathematical strategies are also applied to establish our epidemic model, which is a pandemic model as well. In addition, we mathematically establish the chance for the next wave of any pandemic disease and show that a consistent vaccination strategy could control it. Our proposal is the first model introducing a vaccination strategy to actively infected cases. We are sure this work will serve as the basis for future research on COVID-19 and pandemic diseases since our study also considers the vaccinated population. © 2023 by the authors.

COVID-19 SEIAR Model with Sensitivity Analysis

Beside the unexpected toll of mortality and morbidity caused by COVID-19 worldwide, low- and middle-income countries are more suffering from the devastating issues on economic and social life. This disease has fostered mathematical modelling. In this paper, a SEIAR mathematical model is presented to illustrate how policymakers may apply efficient strategies to end or at least to control the devastating wide spread of COVID-19. © 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

Individual preferences, government policy, and COVID-19: A game-theoretic epidemiological analysis.

Purpose: The ongoing COVID-19 pandemic imposes serious short-term and long-term health costs on populations. Restrictive government policy measures decrease the risks of infection, but produce similarly serious social, mental health, and economic problems. Citizens have varying preferences about the desirability of restrictive policies, and governments are thus forced to navigate this tension in making pandemic policy. This paper analyses the situation facing government using a game-theoretic epidemiological model. Methodology: We classify individuals into health-centered individuals and freedom-centered individuals to capture the heterogeneous preferences of citizens. We first use the extended Susceptible-Exposed-Asymptomatic-Infectious-Recovered (SEAIR) model (adding individual preferences) and the signaling game model (adding government) to analyze the strategic situation against the backdrop of a realistic model of COVID-19 infection. Findings: We find the following: 1. There exists two pooling equilibria. When health-centered and freedom-centered individuals send anti-epidemic signals, the government will adopt strict restrictive policies under budget surplus or balance. When health-centered and freedom-centered individuals send freedom signals, the government chooses not to implement restrictive policies. 2. When governments choose not to impose restrictions, the extinction of an epidemic depends on whether it has a high infection transmission rate; when the government chooses to implement non-pharmacological interventions (NPIs), whether an epidemic will disappear depends on how strict the government's restrictions are. Originality/value: Based on the existing literature, we add individual preferences and put the government into the game as a player. Our research extends the current form of combining epidemiology and game theory. By using both we get a more realistic understanding of the spread of the virus and combine that with a richer understanding of the strategic social dynamics enabled by game theoretic analysis. Our findings have important implications for public management and government decision-making in the context of COVID-19 and for potential future public health emergencies.

Influence of Human Behavior on COVID-19 Dynamics Based on a Reaction-Diffusion Model.

To investigate the influence of human behavior on the spread of COVID-19, we propose a reaction-diffusion model that incorporates contact rate functions related to human behavior. The basic reproduction number R0 is derived and a threshold-type result on its global dynamics in terms of R0 is established. More precisely, we show that the disease-free equilibrium is globally asymptotically stable if R0≤1; while there exists a positive stationary solution and the disease is uniformly persistent if R0>1. By the numerical simulations of the analytic results, we find that human behavior changes may lower infection levels and reduce the number of exposed and infected humans.

Epidemic Management via Imperfect Testing: A Multi-criterial Perspective.

Diagnostic testing may represent a key component in response to an ongoing epidemic, especially if coupled with containment measures, such as mandatory self-isolation, aimed to prevent infectious individuals from furthering onward transmission while allowing non-infected individuals to go about their lives. However, by its own nature as an imperfect binary classifier, testing can produce false negative or false positive results. Both types of misclassification are problematic: while the former may exacerbate the spread of disease, the latter may result in unnecessary isolation mandates and socioeconomic burden. As clearly shown by the COVID-19 pandemic, achieving adequate protection for both people and society is a crucial, yet highly challenging task that needs to be addressed in managing large-scale epidemic transmission. To explore the trade-offs imposed by diagnostic testing and mandatory isolation as tools for epidemic containment, here we present an extension of the classical Susceptible-Infected-Recovered model that accounts for an additional stratification of the population based on the results of diagnostic testing. We show that, under suitable epidemiological conditions, a careful assessment of testing and isolation protocols can contribute to epidemic containment, even in the presence of false negative/positive results. Also, using a multi-criterial framework, we identify simple, yet Pareto-efficient testing and isolation scenarios that can minimize case count, isolation time, or seek a trade-off solution for these often contrasting epidemic management objectives.

Dynamics of a fractional COVID-19 model with immunity using harmonic incidence mean-type.

The transmission dynamics of COVID-19 is investigated through the prism of the Atangana-Baleanu fractional model with acquired immunity. Harmonic incidence mean-type aims to drive exposed and infected populations towards extinction in a finite time frame. The reproduction number is calculated based on the next-generation matrix. A disease-free equilibrium point can be achieved globally using the Castillo-Chavez approach. Using the additive compound matrix approach, the global stability of endemic equilibrium can be demonstrated. Utilizing Pontryagin's maximum principle, we introduce three control variables to obtain the optimal control strategies. Laplace transform allows simulating the fractional-order derivatives analytically. Analysis of the graphical results led to a better understanding of the transmission dynamics.

Dynamics and profiles of a degenerated reaction-diffusion host-pathogen model with apparent and inapparent infection period.

Inapparent infection plays an important role in the disease spread, which is an infection by a pathogen that causes few or no signs or symptoms of infection in the host. Many pathogens, including HIV, typhoid fever, and coronaviruses such as COVID-19 spread in their host populations through inapparent infection. In this paper, we formulated a degenerated reaction-diffusion host-pathogen model with multiple infection period. We split the infectious individuals into two distinct classes: apparent infectious individuals and inapparent infectious individuals, coming from exposed individuals with a ratio of (1-p) and p, respectively. Some preliminary results and threshold-type results are achieved by detailed mathematical analysis. We also investigate the asymptotic profiles of the positive steady state (PSS) when the diffusion rate of susceptible individuals approaches zero or infinity. When all parameters are all constants, the global attractivity of the constant endemic equilibrium is established. It is verified by numerical simulations that spatial heterogeneity of the transmission rates can enhance the intensity of an epidemic. Especially, the transmission rate of inapparent infectious individuals significantly increases the risk of disease transmission, compared to that of apparent infectious individuals and pathogens in the environment, and we should pay special attentions to how to regulate the inapparent infectious individuals for disease control and prevention, which is consistent with the result on the sensitive analysis to the transmission rates through the normalized forward sensitivity index. We also find that disinfection of the infected environment is an important way to prevent and eliminate the risk of environmental transmission.

Co-dynamics of COVID-19 and TB with COVID-19 vaccination and exogenous reinfection for TB: An optimal control application.

COVID-19 and Tuberculosis (TB) are among the major global public health problems and diseases with major socioeconomic impacts. The dynamics of these diseases are spread throughout the world with clinical similarities which makes them difficult to be mitigated. In this study, we formulate and analyze a mathematical model containing several epidemiological characteristics of the co-dynamics of COVID-19 and TB. Sufficient conditions are derived for the stability of both COVID-19 and TB sub-models equilibria. Under certain conditions, the TB sub-model could undergo the phenomenon of backward bifurcation whenever its associated reproduction number is less than one. The equilibria of the full TB-COVID-19 model are locally asymptotically stable, but not globally, due to the possible occurrence of backward bifurcation. The incorporation of exogenous reinfection into our model causes effects by allowing the occurrence of backward bifurcation for the basic reproduction number R0 < 1 and the exogenous reinfection rate greater than a threshold (η > Î·∗). The analytical results show that reducing R0 < 1 may not be sufficient to eliminate the disease from the community. The optimal control strategies were proposed to minimize the disease burden and related costs. The existence of optimal controls and their characterization are established using Pontryagin's Minimum Principle. Moreover, different numerical simulations of the control induced model are carried out to observe the effects of the control strategies. It reveals the usefulness of the optimization strategies in reducing COVID-19 infection and the co-infection of both diseases in the community.

The Transmissibility of Covid-19: A Modelling Study in China

Covid-19 is a serious disease for human. It can be easily spread between human. In order to model the spread of Covid-19 and determinate the appropriate policy by government, I use the SEIRD model, which is extended from SIR model. In this paper, the SEIRD model studies the transmissibility of Covid-19 in China. This work first gives out the flowchart of the SEIRD model and then I derive the differential equation and find out the disease-free equilibrium based on the flowchart. Then I calculate the generation matrix and basic reproduction number which is directly related to the transmissibility of the virus. At last, the sensitivity analysis analyzes the different impact from different parameter. From that, we can find out the best way to control the transmission. The result is that the parameter that refer to strictness has a great impact on the spread of Covid-19. However, it doesn't have to be as large as possible since the covid can be well controlled with an appropriate value of strictness and smallest negative effect for people. This paper tries to find out the best extent of strictness of policy that is able to control the transmission. © 2023 SPIE.

Monitoring the Covid-19 Immune Landscape in Japan

Intro: COVID-19 vaccination in Japan started on February 17, 2021. Because the timing of vaccination and the risk of severe COVID-19 greatly varied with age, the present study aimed to monitor the age-specific fractions of the population who were immune to SARS-CoV-2 infection after vaccination. Method(s): Natural infection remained extremely rare, accounting for less than 5% of the population by the end of 2021;thus, we ignored natural infection- induced immunity and focused on vaccine-induced immunity. We estimated the fraction of the population immune to infection by age group using vaccination registry data from February 17, 2021, to October 17, 2021. We accounted for two important sources of delay: (i) reporting delay and (ii) time from vaccination until immune protection develops. Finding(s): At the end of the observation period, the proportion of individuals still susceptible to SARS-CoV-2 infection substantially varied by age and was estimated to be >=90% among people aged 0-14 years, in contrast to approximately 20% among the population aged >=65 years. We also estimated the effective reproduction number over time using a next-generation matrix while accounting for differences in the proportion immune to infection by age. Discussion(s): The COVID-19 immune landscape greatly varied by age, and a substantial proportion of young adults remained susceptible. Vaccination contributed to a marked decrease in the reproduction number. Conclusion(s): The present study offers a novel approach to monitoring the age- related immune landscape over time in Japan.Copyright © 2023

Modeling The Effect of Contaminated Object, Vaccination and Treatment on The Diseases Epidemiology

In this paper, the effect of contaminated objects on a SIRS Model with vaccination and hospitalization compartments is modeled. Positivity and boundedness properties of the solutions of model are proved, basic reproduction number of the model is founded through criteria which make the eigenvalues of the Jacobean matrix at the disease-free equilibrium point, negative. Globally stability analysis of the disease-free equilibrium point is proved when the basic reproduction number is less than unity. The existence, uniqueness of the endemic equilibrium point is investigated when the basic reproduction number is greater than unity. Parameter values regarding to spreading covid-19 in Kurdistan region are estimated. Finally, sensitivity analysis of the reproduction number is carried out. © 2022 Production by the University of Garmian. This is an open access article under the LICENSE.

High-rise buildings: A risk factor in the COVID-19 Omicron epidemic period.

Objectives: This study aimed to investigate possible viral transmission scenarios inside a high-rise building during the Omicron phase of the COVID-19 pandemic. Study design: Cross-sectional study design. Methods: In order to determine the pathogenicity of the Omicron variant of SARS-CoV-2, demographic, vaccination and clinical data were collected from COVID-19 positive cases during an outbreak in a high-rise residential building in Shenzhen, China, in early 2022. The pattern of viral transmission inside the building was determined through field investigation and engineering analysis. The results highlight the risk of Omicron infection in high-rise residential buildings. Results: Symptoms of infection with the Omicron variant are predominantly mild. Younger age has a greater impact on the severity of disease than vaccination status. Each floor of the high-rise building investigated contained 7 apartments, numbered 01 to 07, positioned in the same layout on each floor. The drainage system included vertical pipes from the ground to the roof of the building. There were statistically significant differences in infection rates at different time points and incidence ratios between apartment numbers ending in 07 (type 07) and other apartments (P < 0.001). Households with early disease onset were concentrated in apartment type 07 and the severity of their disease was more severe. The incubation period of the outbreak was 5.21-5.31 days and the time-dependent reproduction number (Rt) was 12.08 (95% confidence interval [CI] 7.66, 18.29). Results suggest both non-contact and contact viral transmission may have contributed to the outbreak. The drainage system in the building allows aerosol regurgitation, thus indicating that the structure of the building may have led to spread of the virus from the sewage pipes. Infections in other apartments may have been as result of viral transmission in the elevators and intimate family contact. Conclusions: Results from this study suggest that Omicron transmission was likely to be via the sewage system, supplemented by contact transmission in the stairs and elevators. The environmental spread of Omicron needs to be highlighted and prevented.

Age-dependent final size equation to anticipate mortality impact of COVID-19 in China.

Before reopening society in December 2022, China had not achieved sufficiently high vaccination coverage among people aged 80 years and older, who are vulnerable to severe infection and death owing to COVID-19. Suddenly ending the zero-COVID policy was anticipated to lead to substantial mortality. To investigate the mortality impact of COVID-19, we devised an age-dependent transmission model to derive a final size equation, permitting calculation of the expected cumulative incidence. Using an age-specific contact matrix and published estimates of vaccine effectiveness, final size was computed as a function of the basic reproduction number, R0. We also examined hypothetical scenarios in which third-dose vaccination coverage was increased in advance of the epidemic, and also in which mRNA vaccine was used instead of inactivated vaccines. Without additional vaccination, the final size model indicated that a total of 1.4 million deaths (half of which were among people aged 80 years and older) were anticipated with an assumed R0 of 3.4. A 10% increase in third-dose coverage would prevent 30,948, 24,106, and 16,367 deaths, with an assumed second-dose effectiveness of 0%, 10%, and 20%, respectively. With mRNA vaccine, the mortality impact would have been reduced to 1.1 million deaths. The experience of reopening in China indicates the critical importance of balancing pharmaceutical and non-pharmaceutical interventions. Ensuring sufficiently high vaccination coverage is vital in advance of policy changes.

Impact of tiered measures on social contact and mixing patterns of in Italy during the second wave of COVID-19.

BACKGROUND: Most countries around the world enforced non-pharmaceutical interventions against COVID-19. Italy was one of the first countries to be affected by the pandemic, imposing a hard lockdown, in the first epidemic wave. During the second wave, the country implemented progressively restrictive tiers at the regional level according to weekly epidemiological risk assessments. This paper quantifies the impact of these restrictions on contacts and on the reproduction number. METHODS: Representative (with respect to age, sex, and region of residence) longitudinal surveys of the Italian population were undertaken during the second epidemic wave. Epidemiologically relevant contact patterns were measured and compared with pre-pandemic levels and according to the level of interventions experienced by the participants. Contact matrices were used to quantify the reduction in the number of contacts by age group and contact setting. The reproduction number was estimated to evaluate the impact of restrictions on the spread of COVID-19. RESULTS: The comparison with the pre-pandemic baseline shows a significant decrease in the number of contacts, independently from the age group or contact settings. This decrease in the number of contacts significantly depends on the strictness of the non-pharmaceutical interventions. For all levels of strictness considered, the reduction in social mixing results in a reproduction number smaller than one. In particular, the impact of the restriction on the number of contacts decreases with the severity of the interventions. CONCLUSIONS: The progressive restriction tiers implemented in Italy reduced the reproduction number, with stricter interventions associated with higher reductions. Readily collected contact data can inform the implementation of mitigation measures at the national level in epidemic emergencies to come.