Complex Dynamics in an Epidemic Model with Imitation-Driven Vaccination Strategy

Two profitless delays for an SEIRS epidemic disease model with vertical transmission and pulse vaccination

Letters20 October 2020Locally Informed Simulation to Predict Hospital Capacity Needs During the COVID-19 PandemicFREEGary E. Weissman, MD, MSHP, Andrew Crane-Droesch, PhD, Corey Chivers, PhD, Mark E. Mikkelsen, MD, MSCE, and Scott D. Halpern, MD, PhDGary E. Weissman, MD, MSHPUniversity of Pennsylvania, Philadelphia, Pennsylvania (G.E.W., M.E.M., S.D.H.)Search for more papers by this author, Andrew Crane-Droesch, PhDUniversity of Pennsylvania and Penn Medicine Predictive Healthcare, Philadelphia, Pennsylvania (A.C.)Search for more papers by this author, Corey Chivers, PhDPenn Medicine Predictive Healthcare, Philadelphia, Pennsylvania (C.C.)Search for more papers by this author, Mark E. Mikkelsen, MD, MSCEUniversity of Pennsylvania, Philadelphia, Pennsylvania (G.E.W., M.E.M., S.D.H.)Search for more papers by this author, and Scott D. Halpern, MD, PhDUniversity of Pennsylvania, Philadelphia, Pennsylvania (G.E.W., M.E.M., S.D.H.)Search for more papers by this authorAuthor, Article, and Disclosure Informationhttps://doi.org/10.7326/L20-1062 SectionsAboutVisual AbstractPDF ToolsAdd to favoritesDownload CitationsTrack CitationsPermissions ShareFacebookTwitterLinkedInRedditEmail IN RESPONSE:Dr. Stern highlights 2 important limitations of the SIR model that underlie the CHIME planning tool. We agree that the cohort structure—defined by differences in demographic characteristics, disease response, and contact patterns, among others—influences the course and severity of the pandemic. Using an agent-based model with a first-in, first-out process as Dr. Stern suggests would permit the representation of some of these cohort characteristics. However, this approach would come at the cost of increased complexity, with accompanying difficulty in identifying reliable parameter estimates based on limited published data early in the pandemic.The SIR assumption of a constant doubling time does not reflect the effects of rapidly changing physical distancing behaviors and other policies that might alter viral transmission. Thus, we have advised that the CHIME tool be used only for reliable short-term forecasts. We advocate that users of CHIME and any other COVID-19–related pandemic model iteratively review all parameters based on empirical observations of the pandemic course.As our model has been iteratively revised since publication, the subsequent CHIME estimates have also indicated an earlier but not higher peak, as suggested by Dr. Stern's calculations. However, we disagree that the direction of SIR model bias is yet definitely known in the case of COVID-19. The cited article suggests that the SIR model underestimates model peak and timing compared with 1 matrix model (1). At the same time, other work has suggested that SIR models may overestimate total epidemic size compared with contact models that account for social network structure (2). Further work is needed to validate all COVID-19–related pandemic models against both each other and empirically observed counts of infected cases and their subsequent care utilization patterns. As such, our original manuscript included a plan to undertake such an empirical validation.At this time, we again acknowledge the limitations of SIR models and have since extended CHIME to account for more complex dynamics as more data have become available (https://penn-chime.phl.io). The performance of CHIME has improved with updating since publication, and CHIME has so far proved useful to guide planning efforts in our health system. However, we will continue to revise and assess the model in order to apply these lessons to more efficiently and effectively model future epidemics.

A tale of two rhythms: Locked clocks and chaos in biology.

Dynamic complexities in a seasonal prevention epidemic model with birth pulses

Two profitless delays for the SEIRS epidemic disease model with nonlinear incidence and pulse vaccination

This research introduces a new approach utilizing optimal control theory to assess the Social Optimum (SO) of a vaccination game, navigating the intricate considerations of cost, availability, and distribution policies. By integrating an SIRS/V (Susceptible-Infected-Recovered-Susceptible/Vaccinated) epidemic model with a behavior model, the study analyzes individual vaccination strategies. A unique optimal control framework, centered on vaccination costs, is proposed, diverging significantly from previous methods. Our findings confirm the effectiveness and feasibility of this approach in managing vaccination strategies. Moreover, we examine the underlying social dilemma of the vaccination game, investigating key parameters. By calculating the Nash equilibrium (NE) through the behavior model and determining the SO using our approach, we measure the social efficiency deficit, quantifying the overall cost gap between the NE and SO. The results indicate that an increased waning immunity rate exacerbates the social dilemma, although higher vaccination costs partially mitigate it. This research provides valuable insights into optimizing vaccination strategies amid complex societal dynamics.

Epidemic models like the SIS or SIR model enable us to describe simple spreading processes over networks but are often not sufficient to accurately capture more complex network dynamics as exhibited by sophisticated and malicious computer worms. Many of the common assumptions behind epidemic models do not necessary hold if the process under investigation spans big networks or large scales of time. We extend the standard SIS network model by dropping the assumption of a constant curing rate in favour of a time-dependent curing rate function, which enables us to reflect changes in the effectiveness of the active worm removal process over time. The resulting time-dependent mean-field SIS model allows us to study the evolution of the size of computer worm bot-nets. We exemplify the complete procedure, including data-processing, needed to obtain a reliable model on data from Conficker, an extremely resilient computer worm. Using empirical data obtained from the Conficker sinkhole, we fit long time periods of up to 6 years on multiple scales and different levels of noise. We end by reflecting on the limits of epidemic models in empirical analysis of malware threats.

This paper is concerned with complex dynamical behaviors of a simple unified SIR and HIV disease model with a convex incidence and four real parameters. Due to the complex nature of the disease dynamics, our goal is to explore bifurcations including multistable states, limit cycles, and homoclinic loops in the whole parameter space. The first contribution is the proof of the existence of multiple limit cycles giving rise from Hopf bifurcation, which further induces bistable or tristable states because of the coexistence of stable equilibria and periodic motion. Next, we propose that the existence of Bogdanov–Takens (BT) bifurcation yields the bifurcation of homoclinic loops, which provides a new mechanism for generating disease recurrence, for example, the relapse–remission, viral blip cycles in HIV infection. Last, we present a novel method for the derivation of the normal forms of codimension two and three BT bifurcations. The method is based on the simplest normal form theory from Yu’s previous works.

We study an epidemic model with nonlinear incidence rate, describing the saturated mass action and the psychological effect of certain serious diseases on the community. Firstly, the existence and local stability of disease-free and endemic equilibria are investigated. Then we prove the occurrence of backward bifurcations, saddle-node bifurcations, Hopf bifurcations and cusp type Bogdanov–Takens bifurcations of codimension 3. Finally, numerical simulations, including one limit cycle, two limit cycles, an unstable homoclinic loop and many other phase portraits are presented. These results show that the psychological effect of diseases and the behavior change of the susceptible individuals may affect the final spread level of an epidemic.

Approximation methods for analyzing multiscale stochastic vector-borne epidemic models

Complex dynamics and control strategies of SEIR heterogeneous network model with saturated treatment

Impact of contact heterogeneity on initial growth behavior of an epidemic: Complex network-based approach

In this paper, we have proposed and formulated an epidemic model with two types of diseases-one is comparative weaker and the other is comparatively stronger with the assumption that both the diseases are active simultaneously in the system. The dynamical behavior of the model; equilibrium analyses with their existence criteria and local stability criteria have been discussed rigorously. With the help of second generation matrix method, we evaluate basic reproduction number of the proposed model. We propose an optimal control problem considering treatment as control parameter and solve it in order to minimize the compound loss due to the presence of infection. All the theoretical results are verified with some appropriate computer simulation works.

In this study, we have developed a novel SIR epidemic model by incorporating fractional-order differential equations and utilizing saturated-type functions to describe both disease incidence and treatment. The intricate dynamical characteristics of the proposed model, encompassing the determination of the conditions for the existence of all possible feasible equilibria with their local and global stability criteria, are investigated thoroughly. The model undergoes backward bifurcation with respect to the parameter representing the side effects due to treatment. This phenomenon emphasizes the critical role of treatment control parameters in shaping epidemic outcomes. In addition, to understand the optimal role of the treatment in mitigating the disease prevalence and minimizing the associated cost, we investigated a fractional-order optimal control problem. To further visualize the analytical results, we have conducted simulation works considering feasible parameter values for the model. Finally, we have employed local and global sensitivity analysis techniques to identify the factors that have the greatest potential to reduce the impact of the disease.

In this manuscript, we consider an epidemic model having constant recruitment of susceptible individuals with non-monotone disease transmission rate and saturated-type treatment rate. Two types of disease control strategies are taken here, namely vaccination for susceptible individuals and treatment for infected individuals to minimize the impact of the disease. We study local as well as global stability analysis of the disease-free equilibrium point and also endemic equilibrium point based on the values of basic reproduction number R_0. Therefore, disease eradicates from the population if basic reproduction number less than unity and disease persists in the population if basic reproduction number greater than unity. We use center manifold theorem to study the dynamical behavior of the disease-free equilibrium point for R_0 = 1. We investigate different bifurcations such as transcritical bifurcation, backward bifurcation, saddle-node bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation of co-dimension 2. The biological significance of all types of bifurcations are described. Some numerical simulations are performed to check the reliability of our theoretical approach. Sensitivity analysis is performed to identify the influential model parameters which have most impact on the basic reproduction number of the proposed model. To control or eradicate the influence of the emerging disease, we need to control the most sensitive model parameters using necessary preventive measures. We study optimal control problem using Pontryagin’s maximum principle. Finally using efficiency analysis, we determine most effective control strategy among applied controls.