Dynamics of vaccination in a time-delayed epidemic model with awareness

Competitive dual-strain SIS epidemiological models with awareness programs in heterogeneous networks: two modeling approaches

Epidemic diseases and media campaigns are closely associated with each other. Considering most epidemics have multiple pathogenic strains, in this paper, we take the lead in proposing two multi-strain SIS epidemic models in heterogeneous networks incorporating awareness programs due to media. For the first model, we assume that the transmission rates for strain 1 and strain 2 depend on the level of awareness campaigns. For the second one, we further suppose that awareness divides susceptible population into two different subclasses. After defining the basic reproductive numbers for the whole model and each strain, we obtain the analytical conditions that determine the extinction, coexistence and absolute dominance of two strains. Moreover, we also formulate its optimal control problem and identify an optimal implementation pair of awareness campaigns using optimal control theory. Given the complexity of the second model, we use the numerical simulations to visualize its different types of dynamical behaviors. Through theoretical and numerical analysis of these two models, we discover some new phenomena. For example, during the persistence analysis of the first model, we find that the characteristic polynomials of two boundary equilibria may have a pair of pure imaginary roots, implying that Hopf bifurcation and periodic solutions may appear. Most strikingly, multistability occurs in the second model and the growth rate of awareness programs (triggered by the infection prevalence) has a multistage impact on the final size of two strains. The numerical results suggest that the spread of a two-strain epidemic can be controlled (even be eradicated) by taking the measures of enhancing awareness transmission, reducing memory fading of aware individuals and ensuring high-level influx and rapid growth of awareness programs appropriately.

Modeling the effect of health education and individual participation on the increase of sports population and optimal design

Health education plays an important role in cultivating people's awareness of participating in physical exercise. In this paper, a new differential equation model is established to dynamically demonstrate the different impact of mass communication and interpersonal communication in health education on people's participation in physical exercise. Theoretical analysis shows that health education does not affect the system threshold, but individual participation does. The combination of the two leads to different equilibria and affects the stability of equilibria. When mass communication, interpersonal communication and individual participation satisfy different conditions, the system will obtain different positive equilibrium with different number of sports population. If the interpersonal transmission rate of information is bigger, there is a positive equilibrium with a large number of sports population in the system. Sensitivity and optimal design analysis show some interesting results. First, increasing interpersonal communication and mass communication can both increase the number of conscious non-sports population and sports population. For increasing the number of conscious non-sports population, the effect of mass communication is better than that of interpersonal communication. For increasing the number of sports population, the effect of interpersonal communication is better than that of mass communication. However, individual participation has the best effect on increasing the sports population. Second, increasing the daily fixed amount of new information will be more helpful for media information dissemination. Finally, the three control measures need to be implemented simultaneously for a period of time at first, and then health education and participation of sports people need to be implemented periodically in order to maximize the sports population.

Global dynamics of an SIS compartment model with resource constraints

This paper formulates a mathematical framework to describe the dynamics of SIS-type infectious diseases with resource constraints. We first define the basic reproduction number that determines disease prevalence and analyze the existence and local stability of the equilibria. Subsequently, we analyze the global dynamics of the model, excluding periodic solutions and heteroclinic orbits, using the compound matrix approach. The analysis implies that the model can undergo forward and backward bifurcations depending on critical parameters. In the former scenario, the disease persists when the basic reproduction number under resource constraints exceeds one. In the latter scenario, the backward bifurcation creates bistability dynamics in which the disease may persist or become extinct depending on the initial level of infected individuals and the resource abundance.

FOMO (fate of online media only) in infectious disease modeling: a review of compartmental models

Mathematical models played in a major role in guiding policy decisions during the COVID-19 pandemic. These models while focusing on the spread and containment of the disease, largely ignored the impact of media on the disease transmission. Media plays a major role in shaping opinions, attitudes and perspectives and as the number of people online increases, online media are fast becoming a major source for news and health related information and advice. Consequently, they may influence behavior and in due course disease dynamics. Unlike traditional media, online media are themselves driven and influenced by their users and thus have unique features. The main techniques used to incorporate online media mathematically into compartmental models, with particular reference to the ongoing COVID-19 pandemic are reviewed. In doing so, features specific to online media that have yet to be fully integrated into compartmental models such as misinformation, different time scales with regards to disease transmission and information, time delays, information super spreaders, the predatory nature of online media and other factors are identified together with recommendations for their incorporation.

Mathematical modeling and stability analysis of the time-delayed SAIM model for COVID-19 vaccination and media coverage

Since the COVID-19 outbreak began in early 2020, it has spread rapidly and threatened public health worldwide. Vaccination is an effective way to control the epidemic. In this paper, we model a SAIM equation. Our model involves vaccination and the time delay for people to change their willingness to be vaccinated, which is influenced by media coverage. Second, we theoretically analyze the existence and stability of the equilibria of our model. Then, we study the existence of Hopf bifurcation related to the two equilibria and obtain the normal form near the Hopf bifurcating critical point. Third, numerical simulations based two groups of values for model parameters are carried out to verify our theoretical analysis and assess features such as stable equilibria and periodic solutions. To ensure the appropriateness of model parameters, we conduct a mathematical analysis of official data. Next, we study the effect of the media influence rate and attenuation rate of media coverage on vaccination and epidemic control. The analysis results are consistent with real-world conditions. Finally, we present conclusions and suggestions related to the impact of media coverage on vaccination and epidemic control.

Analyzing COVID-19 Vaccination Behavior Using an SEIRM/V Epidemic Model With Awareness Decay

Information awareness about COVID-19 spread through multiple channels can stimulate individuals to vaccinate to protect themselves and reduce the infection rate. However, the awareness individuals may lose competency over time due to the decreasing quality of the information and fading of awareness. This paper introduces awareness programs, which can not only change people from unaware to aware state, but also from aware to unaware state. Then an SEIRM/V mathematical model is derived to study the influence of awareness programs on individual vaccination behavior. We evaluate the dynamical evolution of the system model and perform the numerical simulation, and examine the effects of awareness transformation based on the COVID-19 vaccination case in China. The results show that awareness spread through various information sources is positively associated with epidemic containment while awareness fading negatively correlates with vaccination coverage.

Delay in budget allocation for vaccination and awareness induces chaos in an infectious disease model

In this paper, we propose a model to assess the impacts of budget allocation for vaccination and awareness programs on the dynamics of infectious diseases. The budget allocation is assumed to follow logistic growth, and its per capita growth rate increases proportional to disease prevalence. An increment in per-capita growth rate of budget allocation due to increase in infected individuals after a threshold value leads to onset of limit cycle oscillations. Our results reveal that the epidemic potential can be reduced or even disease can be eradicated through vaccination of high quality and/or continuous propagation of awareness among the people in endemic zones. We extend the proposed model by incorporating a discrete time delay in the increment of budget allocation due to infected population in the region. We observe that multiple stability switches occur and the system becomes chaotic on gradual increase in the value of time delay.

Vaccination control of an epidemic model with time delay and its application to COVID-19

This paper studies an SEIR-type epidemic model with time delay and vaccination control. The vaccination control is applied when the basic reproduction number R 0 > 1 . The vaccination strategy is expressed as a state delayed feedback which is related to the current and previous state of the epidemic model, and makes the model become a linear system in new coordinates. For the presence and absence of vaccination control, we investigate the nonnegativity and boundedness of the model, respectively. We obtain some sufficient conditions for the eigenvalues of the linear system such that the nonnegativity of the epidemic model can be guaranteed when the vaccination strategy is applied. In addition, we study the stability of disease-free equilibrium when R 0 < 1 and the persistent of disease when R 0 > 1 . Finally, we use the obtained theoretical results to simulate the vaccination strategy to control the spread of COVID-19.

A time-delayed SVEIR model for imperfect vaccine with a generalized nonmonotone incidence and application to measles

In this paper, we investigate the effects of the latent period on the dynamics of infectious disease with an imperfect vaccine. We assume a general incidence rate function with a non-monotonicity property to interpret the psychological effect in the susceptible population when the number of infectious individuals increases. After we propose the model, we provide the well-posedness property by verifying the non-negativity and boundedness of the models solutions. Then, we calculate the effective reproduction number R E . The threshold dynamics of the system is obtained with respect to R E . We discuss the global stability of the disease-free equilibrium when R E < 1 and explore the system persistence when R E > 1 . Moreover, we prove the coexistence of an endemic equilibrium when the system persists. Then, we discuss the critical vaccination coverage rate that is required to eliminate the disease. Numerical simulations are provided to: (i) implement a case study regarding the measles disease transmission in the United States from 1963 to 2016; (ii) study the local and global sensitivity of R E with respect to the model parameters; (iii) discuss the stability of endemic equilibrium; and (iv) explore the sensitivity of the proposed model solutions with respect to the main parameters.

The value of infectious disease modeling and trend assessment: a public health perspective

INTRODUCTION

Disease outbreaks of acquired immunodeficiency syndrome, severe acute respiratory syndrome, pandemic H1N1, H7N9, H5N1, Ebola, Zika, Middle East respiratory syndrome, and recently COVID-19 have raised the attention of the public over the past half-century. Revealing the characteristics and epidemic trends are important parts of disease control. The biological scenarios including transmission characteristics can be constructed and translated into mathematical models, which can help to predict and gain a deeper understanding of diseases.

AREAS COVERED

This review discusses the models for infectious diseases and highlights their values in the field of public health. This information will be of interest to mathematicians and clinicians, and make a significant contribution toward the development of more specific and effective models. Literature searches were performed using the online database of PubMed (inception to August 2020).

EXPERT OPINION

Modeling could contribute to infectious disease control by means of predicting the scales of disease epidemics, indicating the characteristics of disease transmission, evaluating the effectiveness of interventions or policies, and warning or forecasting during the pre-outbreak of diseases. With the development of theories and the ability of calculations, infectious disease modeling would play a much more important role in disease prevention and control of public health.

Threshold dynamics of a time-delayed epidemic model for continuous imperfect-vaccine with a generalized nonmonotone incidence rate

In this paper, we study the dynamics of an infectious disease in the presence of a continuous-imperfect vaccine and latent period. We consider a general incidence rate function with a non-monotonicity property to interpret the psychological effect in the susceptible population. After we propose the model, we provide the well-posedness property and calculate the effective reproduction number R E . Then, we obtain the threshold dynamics of the system with respect to R E by studying the global stability of the disease-free equilibrium when R E < 1 and the system persistence when R E > 1 . For the endemic equilibrium, we use the semi-discretization method to analyze its linear stability. Then, we discuss the critical vaccination coverage rate that is required to eliminate the disease. Numerical simulations are provided to implement a case study regarding data of influenza patients, study the local and global sensitivity of R E < 1 , construct approximate stability charts for the endemic equilibrium over different parameter spaces and explore the sensitivity of the proposed model solutions.

Coevolution spreading in complex networks

The propagations of diseases, behaviors and information in real systems are rarely independent of each other, but they are coevolving with strong interactions. To uncover the dynamical mechanisms, the evolving spatiotemporal patterns and critical phenomena of networked coevolution spreading are extremely important, which provide theoretical foundations for us to control epidemic spreading, predict collective behaviors in social systems, and so on. The coevolution spreading dynamics in complex networks has thus attracted much attention in many disciplines. In this review, we introduce recent progress in the study of coevolution spreading dynamics, emphasizing the contributions from the perspectives of statistical mechanics and network science. The theoretical methods, critical phenomena, phase transitions, interacting mechanisms, and effects of network topology for four representative types of coevolution spreading mechanisms, including the coevolution of biological contagions, social contagions, epidemic-awareness, and epidemic-resources, are presented in detail, and the challenges in this field as well as open issues for future studies are also discussed.

Study on a susceptible–infected–vaccinated model with delay and proportional vaccination

A susceptible–infected–vaccinated epidemic model with proportional vaccination and generalized nonlinear rate is formulated and investigated in the paper. We show that the stochastic epidemic model admits a unique and global positive solution with probability one when constructing a proper [Formula: see text]-function therewith. Then a sufficient condition that guarantees the disappearances of diseases is derived when the indicator [Formula: see text]. Further, if [Formula: see text], then we obtain that the solution is weakly permanent with probability one. We also derived the sufficient conditions of the persistence in the mean for the susceptible and infected when another indicator [Formula: see text].