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In this paper, we construct an infectious disease model with a testing compartment and analyze the existence and stability of its endemic states. We obtain the basic reproduction number, R 0 , and demonstrate the existence of one endemic equilibrium without testing and one endemic equilibrium with testing and prove their local and global stabilities based on the value of the basic reproduction number, R 0 . We then apply our model to the US COVID-19 pandemic and find that, for a large parameter set, including those relevant to the SARS-CoV-2 virus, our analytic and numerical results suggest that the trajectories will be trapped to the testing-free state when the testing number is small enough. This indicates that the pandemic may end with a testing-free endemic state through a novel and surprising mechanism called stochastic trapping. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical model based on COVID-19 is developed to study and manage disease outbreaks. The effect of vaccination with regard to its efficacy and percentage of population vaccinated in a closed population is investigated. To study virus transmission, the system employs six nonlinear ordinary differential equations with susceptible–exposed–asymptomatic–infected–vaccinated–recovered populations and the basic reproduction number are calculated. The proposed model describes for highly infectious diseases (such as COVID-19) in a closed containment area with no migration. This paper considers that the percentage of vaccinated population has a significant impact on the number of COVID-19 positive cases during the pandemic wave and examines how the pandemic rise time is delayed. Numerical simulation to investigate disease outbreaks when the community is undergoing vaccination is performed, taking the efficacy rate of the vaccine into account. Sensitivity Index values are calculated for the reproduction number and their relations with few other parameters are depicted. [ABSTRACT FROM AUTHOR]

Based on China's summary of three years of experience and measures in the prevention and control of the COVID-19 epidemic, we have built a COVID-19 prevention and control model integrating health and medical detection, big data information technology to track the trend of the epidemic throughout the whole process, isolation of key epidemic areas, and dynamic prevention and control management throughout the whole process. This model provides a simple, feasible, and theoretically reliable prevention and control model for future large-scale infectious disease prevention and control. The Lyapnov functional method is replaced by the global exponential attractor theory, which provides a new mathematical method for studying the global stability of the multi parameter, multi variable infectious disease prevention and control system. We extracted mathematical methods and models suitable for non-mathematical infectious disease researchers from profound and difficult to understand mathematical theories. Using the results of the global exponential Attractor theory obtained in this paper, we studied the global dynamics of the COVID-19 model with an epidemiological investigation. The results demonstrated that the non-constant disease-free equilibrium is globally asymptotically stable when λ * < 0 , and the COVID-19 epidemic is persisting uniformly when λ * > 0 . In order to understand the impact of the epidemiological investigation under different prevention and control stages in China, we compare the control effects of COVID-19 under different levels of epidemiological investigation policies. We visually demonstrate the global stability and global exponential attractiveness of the COVID-19 model with transferors between regions and epidemiological investigation in a temporal-spatial heterogeneous environment with the help of numerical simulations. We find that the epidemiological investigation really has a significant effect on the prevention and control of the epidemic situation, and we can also intuitively observe the relationship between the flow of people (including tourism, shopping, work and so on) and epidemiological investigation policies. Our model is adapted to different stages of prevention and control; the emergency "circuit breaker" mechanism of the model is also consistent with actual prevention and control. [ABSTRACT FROM AUTHOR]

Nowadays, a lot of research papers are concentrating on the diffusion dynamics of infectious diseases, especially the most recent one: COVID-19. The primary goal of this work is to explore the stability analysis of a new version of the S E I R model formulated with incommensurate fractional-order derivatives. In particular, several existence and uniqueness results of the solution of the proposed model are derived by means of the Picard–Lindelöf method. Several stability analysis results related to the disease-free equilibrium of the model are reported in light of computing the so-called basic reproduction number, as well as in view of utilising a certain Lyapunov function. In conclusion, various numerical simulations are performed to confirm the theoretical findings. [ABSTRACT FROM AUTHOR]

In this paper, we explore two modeling approaches to understanding the dynamics of infectious diseases in the population: equation-based modeling (EBM) and agent-based modeling (ABM). To achieve this, a comparative study of these approaches was conducted and we highlighted their advantages and disadvantages. Two case studies on the spread of the COVID-19 pandemic were carried out using both approaches. The results obtained show that differential equation-based models are faster but still simplistic, while agent-based models require more machine capabilities but are more realistic and very close to biology. Based on these outputs, it seems that the coupling of both approaches could be an interesting compromise. [ABSTRACT FROM AUTHOR]

In this paper, a hybrid SEIAM model for infectious disease with a continuous age structure is established, where combined dynamic effects of media coverage and multi-staged infected progression on threshold dynamics are discussed. Sufficient conditions for uniform persistence of the solution are studied by using the basic reproduction number. By constructing appropriate Lyapunov functions, the global stability analysis of endemic equilibrium is investigated based on Lyapunov–LaSalle's stability theorem. In order to minimize costs incurred due to applied controls and infectious disease burden, an optimal cost-effective control strategy associated with disease treatment and media coverage is discussed. Numerical simulations are carried out to show consistency with theoretical analysis. [ABSTRACT FROM AUTHOR]

The fractional-order calculus model is suitable for describing real-world problems that contain non-local effects and have memory genetic effects. Based on the definition of the Caputo derivative, the article proposes a class of fractional hepatitis B epidemic model with a general incidence rate. Firstly, the existence, uniqueness, positivity and boundedness of model solutions, basic reproduction number, equilibrium points, and local stability of equilibrium points are studied employing fractional differential equation theory, stability theory, and infectious disease dynamics theory. Secondly, the fractional necessary optimality conditions for fractional optimal control problems are derived by applying the Pontryagin maximum principle. Finally, the optimization simulation results of fractional optimal control problem are discussed. To control the spread of the hepatitis B virus, three control variables (isolation, treatment, and vaccination) are applied, and the optimal control theory is used to formulate the optimal control strategy. Specifically, by isolating infected and non-infected people, treating patients, and vaccinating susceptible people at the same time, the number of hepatitis B patients can be minimized, the number of recovered people can be increased, and the purpose of ultimately eliminating the transmission of hepatitis B virus can be achieved. [ABSTRACT FROM AUTHOR]

This paper analyses an SIRS epidemic model with the vaccination of susceptible individuals and treatment of infectious ones. Both actions are governed by a designed control system whose inputs are the subpopulations of the epidemic model. In addition, the vaccination of a proportion of newborns is considered. The control reproduction number R c of the controlled epidemic model is calculated, and its influence in the existence and stability of equilibrium points is studied. If such a number is smaller than a threshold value R ¯ c , then the model has a unique equilibrium point: the so-called disease-free equilibrium point at which there are not infectious individuals. Furthermore, such an equilibrium point is locally and globally asymptotically stable. On the contrary, if R c > R ¯ c , then the model has two equilibrium points: the referred disease-free one, which is unstable, and an endemic one at which there are infectious individuals. The proposed control strategy provides several free-design parameters that influence both values R c and R ¯ c . Then, such parameters can be appropriately adjusted for guaranteeing the non-existence of the endemic equilibrium point and, in this way, eradicating the persistence of the infectious disease. [ABSTRACT FROM AUTHOR]

Measles is a highly contagious viral disease that can lead to serious complications, including death, particularly in young children. In this study, we developed a mathematical model that incorporates a seasonal transmission parameter to examine the measles transmission dynamics. We define the basic reproduction number ( R 0 ) and show its utility as a threshold parameter for global dynamics and the existence of periodic solutions. The model was applied to the measles outbreak that occurred in Pakistan from 2019 to 2021 and provided a good fit to the observed data. Our estimate of the basic reproduction number was found to be greater than one, indicating that the disease will persist in the population. The findings highlight the need to increase vaccination coverage and efficacy to mitigate the impact of the epidemic. The model also shows the long-term behavior of the disease, which becomes endemic and recurs annually. Our simulations demonstrate that a shorter incubation period accelerates the spread of the disease, while a higher vaccination coverage rate reduces its impact. The importance of the second dose of the measles vaccine is emphasized, and a higher vaccine efficacy rate can also help bring R 0 below one. Our study provides valuable information for the development and implementation of effective measles control strategies. To prevent future outbreaks, increasing vaccination coverage among the population is the most effective way to reduce the transmission of measles. [ABSTRACT FROM AUTHOR]

Vaccination is an essential tool for the management of infectious diseases. However, many vaccines are imperfect, having only a partial protective effect in decreasing disease transmission and/or favouring recovery of infected individuals and possibly exhibiting a trade-off between these two properties. Furthermore, the success of vaccination also depends on the population turnover, and the rate of entry to and exit from the population. We here investigate by means of a mathematical model the interplay between these factors to predict optimal vaccination strategies. We first compute the basic reproduction number and study the global stability of the equilibria. We then assess the most influential parameters determining the total number of infected over time using a sensitivity analysis. We derive conditions for the vaccination coverage and efficiency to achieve disease eradication, assuming different intensities of population turnover (weak and strong), vaccine properties (transmission and/or recovery) and the trade-off between the latter. We show that the minimum vaccination coverage increases with lower population turnover decreases with higher vaccine efficiency (transmission or recovery) and is increased/decreased by up to 15% depending on the vaccine trade-off. We conclude that the coverage target for vaccination campaigns should be evaluated based on the interplay between these factors. [ABSTRACT FROM AUTHOR]