Epidemic Dynamics Research Articles

Enhancing vaccination strategies for epidemic control through effective lockdown measures

Evolutionary epidemiology models have substantially impacted the study of various infections and prevention methods in the biology field. These models are called Susceptible, Lockdown, Vaccinated, Infected, and Recovered (SLVIR) epidemic dynamics. We explore how human behavior, particularly in the context of disease transmission, is influenced by two intervention strategies: vaccination and lockdown, both of which are grounded in the principles of evolutionary game theory (EGT). This comprehensive study using evolutionary game theory delves into the dynamics of epidemics, explicitly focusing on the transition rate from susceptibility to immunity and susceptibility to lockdown measures. Our research involves a thorough analysis of the structural aspects of the SLVIR epidemic model, which delineates disease-free equilibria to ensure stability in the system. Our investigation supports the notion that implementing lockdown measures effectively reduces the required level of vaccinations to curtail the prevalence of new infections. Furthermore, it highlights that combining both strategies is particularly potent when an epidemic spreads rapidly. In regions where the disease spreads comparatively more, our research demonstrates that lockdown measures are more effective in reducing the spread of the disease than relying solely on vaccines. Through significant numerical simulations, our research illustrates that integrating lockdown measures and efficient vaccination strategies can indirectly lower the risk of infection within the population, provided they are both dependable and affordable. The outcomes reveal a nuanced and beneficial scenario where we examine the interplay between the evolution of vaccination strategies and lockdown measures, assessing their coexistence through indicators of average social payoff.

A novel indicator in epidemic monitoring through a case study of Ebola in West Africa (2014-2016).

The E/S (exposed/susceptible) ratio is analyzed in the SEIR model. The ratio plays a key role in understanding epidemic dynamics during the 2014-2016 Ebola outbreak in Sierra Leone and Guinea. The maximum value of the ratio occurs immediately before or after the time-dependent reproduction number (Rt) equals 1, depending on the initial susceptible population (S(0)). It is demonstrated that transmission rate curves corresponding to various incubation periods intersect at a single point referred to as the Cross Point (CP). At this point, the E/S ratio reaches an extremum, signifying a critical shift in transmission dynamics and aligning with the time when Rt approaches 1. By plotting transmission rate curves, β(t), for any two arbitrary incubation periods and tracking their intersections, we can trace CP over time. CP serves as an indicator of epidemic status, especially when Rt is close to 1. It provides a practical means of monitoring epidemics without prior knowledge of the incubation period. Through a case study, we estimate the transmission rate and reproduction number, identifying CP and Rt = 1 while examining the E/S ratio across various values of S(0).

Antigenic drift and subtype interference shape A(H3N2) epidemic dynamics in the United States.

Influenza viruses continually evolve new antigenic variants, through mutations in epitopes of their major surface proteins, hemagglutinin (HA) and neuraminidase (NA). Antigenic drift potentiates the reinfection of previously infected individuals, but the contribution of this process to variability in annual epidemics is not well understood. Here we link influenza A(H3N2) virus evolution to regional epidemic dynamics in the United States during 1997-2019. We integrate phenotypic measures of HA antigenic drift and sequence-based measures of HA and NA fitness to infer antigenic and genetic distances between viruses circulating in successive seasons. We estimate the magnitude, severity, timing, transmission rate, age-specific patterns, and subtype dominance of each regional outbreak and find that genetic distance based on broad sets of epitope sites is the strongest evolutionary predictor of A(H3N2) virus epidemiology. Increased HA and NA epitope distance between seasons correlates with larger, more intense epidemics, higher transmission, greater A(H3N2) subtype dominance, and a greater proportion of cases in adults relative to children, consistent with increased population susceptibility. Based on random forest models, A(H1N1) incidence impacts A(H3N2) epidemics to a greater extent than viral evolution, suggesting that subtype interference is a major driver of influenza A virus infection dynamics, presumably via heterosubtypic cross-immunity.

Importance of social inequalities to contact patterns, vaccine uptake, and epidemic dynamics.

Individuals' socio-demographic and economic characteristics crucially shape the spread of an epidemic by largely determining the exposure level to the virus and the severity of the disease for those who got infected. While the complex interplay between individual characteristics and epidemic dynamics is widely recognised, traditional mathematical models often overlook these factors. In this study, we examine two important aspects of human behaviour relevant to epidemics: contact patterns and vaccination uptake. Using data collected during the COVID-19 pandemic in Hungary, we first identify the dimensions along which individuals exhibit the greatest variation in their contact patterns and vaccination uptake. We find that generally higher socio-economic groups of the population have a higher number of contacts and a higher vaccination uptake with respect to disadvantaged groups. Subsequently, we propose a data-driven epidemiological model that incorporates these behavioural differences. Finally, we apply our model to analyse the fourth wave of COVID-19 in Hungary, providing valuable insights into real-world scenarios. By bridging the gap between individual characteristics and epidemic spread, our research contributes to a more comprehensive understanding of disease dynamics and informs effective public health strategies.

Effect of ratio threshold control on epidemic dynamics: analysis of an SIR model with non-monotonic incidence

Effect of ratio threshold control on epidemic dynamics: analysis of an SIR model with non-monotonic incidence

Fractional-Order Dynamics in Epidemic Disease Modeling with Advanced Perspectives of Fractional Calculus

Piecewise fractional-order differential operators have received more attention in recent years because they can be used to describe various evolutionary dynamical problems to investigate crossover behaviors. In this manuscript, we use the aforementioned operators to investigate a mathematical model of COVID-19. By utilizing fractional calculus, our approach aims to capture the crossover dynamics of disease spread, considering heterogeneity and transitions between epidemic phases. This research seeks to develop a framework using specialized mathematical techniques, such as the Caputo fractional derivative, with the potential to investigate the crossover dynamical behaviors of the considered epidemic model. The anticipated contribution lies in bridging fractional calculus and epidemiology, offering insights for both theoretical advancements and practical public health interventions. In order to improve our understanding of epidemic dynamics and support, we used MATLAB to simulate numerical results for a visual representation of our findings. For this interpretation, we used various fractional-order values. In addition, we also compare our simulated results with some reported results for infected and death classes to demonstrate the efficiency of our numerical method.

Wiener and Lévy processes to prevent disease outbreaks: Predictable vs stochastic analysis

The study considers stochastic behavior along with modeling, mathematical analysis, theory development, and numerical simulation of the COVID-19 virus. To evaluate current trends and make future projections regarding the basic reproduction number and infection case, we have taken the modified five-compartment SEIRD mathematical model. Since the basic reproduction number R0 is not sufficient to predict the outbreak, we applied the Itô stochastic differential equations (SDEs) along with the Weiner process and Lévy jump to investigate the nature of the disease outbreak. Since COVID-19 is an infectious disease caused by the severe acute respiratory syndrome coronavirus 2 “(SARS-CoV-2)”, that has common symptoms including fever, cough, and difficulty breathing, we have illustrated the boundedness and positivity of solutions and investigated the stability of endemic and disease-free equilibrium points. The findings show that the dynamics of disease epidemics are influenced by contact patterns. For all the models, the threshold quantity, R0 is calculated which is the key reason to prove the global and local stability analysis of disease-free equilibrium and endemic equilibrium points. Using the least squares method for data fitting, we have performed a case study on COVID-19 data in Italy for this article. A sensitivity analysis is part of our investigation to find important factors. This paper investigates a stochastic epidemic model (SDE) using Lévy jumps and Weiner processes. Local and global stability in a stochastic setting are examined in the analysis. To view the analytical study, a multitude of numerical results are achieved. The study is important to comprehend the stochastic behavior of the virus in the contagious model in order to prevent similar disease outbreaks in the future.

Variance of the Infection Number of Heterogeneous Malware Spread in Network

The Susceptible–Infected–Susceptible (SIS) model in complex networks is one of the critical models employed in the modeling of virus spread. The study of the heterogeneous SIS model with a non-homogeneous nodal infection rate in finite-size networks has attracted little attention. Investigating the statistical properties of heterogeneous SIS epidemic dynamics in finite networks is thus intriguing. In this paper, we focus on the measure of variability in the number of infected nodes for the heterogeneous SIS epidemic dynamics in finite-size bipartite graphs and star graphs. Specifically, we investigate the metastable-state variance of the number of infected nodes for the SIS epidemic process in finite-size bipartite graphs and star graphs with heterogeneous nodal infection rates. We employ an extended individual-based mean-field approximation to analyze the heterogeneous SIS epidemic process in finite-size bipartite networks and star graphs. We derive the approximation solutions of the variance of the infected number. We verify the proposed theory by simulations. The proposed theory has the potential to help us better understand the fluctuations of SIS models like epidemic dynamics with a non-homogeneous infection rate.

Epidemic dynamics of cholera with impulsive sanitation

In this work, we develop an ordinary differential equation (ODE) model with impulsive sanitation of cholera. The sanitation interventions are classified into three types in this article. The first two types are human sanitation, with type-1 sanitation focused on the prevention of direct and indirect transmissions and type-2 focused on prevention of bacterial shedding. The third type refers to pathogen sanitation where interventions are performed in contaminated water environment via disinfection. For the developed impulsive model, we introduce the basic production number R0 and show that R0 remains a sharp disease threshold parameter despite the incorporation of impulsive sanitation. We numerically investigate the impact of impulsive sanitation on the prevention and control of the disease. Our numerical results indicate that type-1 sanitation tends to bear the longest time window between subsequent interventions among all the three types of sanitation provided the same level of sanitation efficacy. Particularly, when the sanitation efficacy is 50% under 90% compliance, type-1 sanitation can be implemented about every 7 months for the purpose of disease control, whereas type-2 and type-3 sanitation will have be performed on a daily basis and every three weeks or so, respectively.

Multicentral Agent-Based Model of Six Epidemic Waves of COVID-19 in the Nizhny Novgorod Region of Russian Federation

Relevance. To investigate the characteristics of the COVID-19 pandemic and introduce timely and effective measures, there is a need for models that can predict the impact of various restrictive actions or characteristics of disease itself on COVID-19 spread dynamics. Employing agent-based models can be attractive because they take into consideration different population characteristics (e.g., age distribution and social activity) and restrictive measures, laboratory testing, etc., as well as random factors that are usually omitted in traditional modifications of the SIR-like dynamic models. Aim. Improvement of the previously proposed agent-based model [23,24] for modeling the spread of COVID-19 in various regions of the Russian Federation. At this stage, six waves of the spread of COVID-19 have been modeled in the Nizhny Novgorod region as a whole region, as well as in its individual cities, taking into account restrictive measures and vaccination of the population. Materials and Methods. In this paper we extend a recently proposed agent-based model for Monte Carlo-based numerical simulation of the spread of COVID-19 with consideration of testing and vaccination strategies. Analysis is performed in MATLAB/ GNU Octave. Results. Developed multicentral model allows for more accurate simulation of the epidemic dynamics within one region, when a patient zero usually arrives at a regional center, after which the distribution chains capture the periphery of the region due to pendulum migration. Furthermore, we demonstrate the application of the developed model to analyze the epidemic spread in the Nizhny Novgorod region of Russian Federation. The simulated dynamics of the daily newly detected cases and COVID-19-related deaths was in good agreement with the official statistical data both for the region as whole and different periphery cities. Conclusions. The results obtained with developed model suggest that the actual number of COVID-19 cases might be 1.5–3.0 times higher than the number of reported cases. The developed model also took into account the effect of vaccination. It is shown that with the same modeling parameters, but without vaccination, the third and fourth waves of the epidemic would be united into one characterized by a huge rise in the morbidity rates and the occurrence of natural individual immunity with the absence of further pandemic waves. Nonetheless, the number of deaths would exceed the real one by about 9–10 times.

Qualitative analysis of solutions for a degenerate partial differential equations model of epidemic spread dynamics

Compartmental models are widely used in mathematical epidemiology to describe the dynamics of infectious diseases or in mathematical models of population genetics. In this study, we study a time-dependent Susceptible-Infectious-Susceptible (SIS) Partial Differential Equation (PDE) model that is based on a diffusion-drift approximation of a probability density from a well-known discrete-time Markov chain model. This SIS-PDE model is conservative due to the degeneracy of the diffusion term at the origin. The main results of this article are the qualitative behavior of weak solutions, the dependence of the local asymptotic property of these solutions on initial data, and the existence of Dirac delta function type solutions. Moreover, we study the long-term behavior of solutions and confirm our analysis with numerical computations.

Statistical methods for the computation and parameter estimation of a fractional SIRC model with Salmonella infection

This study analyzes the fractional order SIRC epidemic model under stochastic fractional differential equations in the Caputo sense. This article describes Salmonella infection in animal herds. For the deterministic system, we explain solution positivity and boundness. We also prove that the fractional stochastic solution exists and is unique. Other criteria considered include non-negativity of solutions, local and global stability analyses, Hyers-Ulam stability analysis, and sensitivity analysis for the deterministic system. Furthermore, according to the truncated Ito-Taylor expansion, we apply a numerical method to solve the stochastic fractional SIRC epidemic model, namely the Milstein method, to solve the stochastic fractional SIRC epidemic model. A comparison of the approximation solution and the corresponding deterministic model for different sample paths shows the efficiency of the numerical method. In addition, graphs and error tables provide insight into numerical experiments' results. The stochastic nature of the model allows random fluctuations in Salmonella infection spread. By incorporating uncertainty into the model, we gain a more realistic understanding of the epidemic dynamics and can better evaluate the effectiveness of control measures. Additionally, the numerical method used to solve the stochastic fractional SIRC epidemic model provides valuable insights into the variability of the results. This enhances our ability to make informed decisions about managing and preventing bacterial infections in animal herds.

Identification and epidemiological study of an uncultured flavivirus from ticks using viral metagenomics and pseudoinfectious viral particles

During their blood-feeding process, ticks are known to transmit various viruses to vertebrates, including humans. Recent viral metagenomic analyses using next-generation sequencing (NGS) have revealed that blood-feeding arthropods like ticks harbor a large diversity of viruses. However, many of these viruses have not been isolated or cultured, and their basic characteristics remain unknown. This study aimed to present the identification of a difficult-to-culture virus in ticks using NGS and to understand its epidemic dynamics using molecular biology techniques. During routine tick-borne virus surveillance in Japan, an unknown flaviviral sequence was detected via virome analysis of host-questing ticks. Similar viral sequences have been detected in the sera of sika deer and wild boars in Japan, and this virus was tentatively named the Saruyama virus (SAYAV). Because SAYAV did not propagate in any cultured cells tested, single-round infectious virus particles (SRIP) were generated based on its structural protein gene sequence utilizing a yellow fever virus-based replicon system to understand its nationwide endemic status. Seroepidemiological studies using SRIP as antigens have demonstrated the presence of neutralizing antibodies against SAYAV in sika deer and wild boar captured at several locations in Japan, suggesting that SAYAV is endemic throughout Japan. Phylogenetic analyses have revealed that SAYAV forms a sister clade with the Orthoflavivirus genus, which includes important mosquito- and tick-borne pathogenic viruses. This shows that SAYAV evolved into a lineage independent of the known orthoflaviviruses. This study demonstrates a unique approach for understanding the epidemiology of uncultured viruses by combining viral metagenomics and pseudoinfectious viral particles.

Stochastic Compartment Model with Mortality and Its Application to Epidemic Spreading in Complex Networks.

We study epidemic spreading in complex networks by a multiple random walker approach. Each walker performs an independent simple Markovian random walk on a complex undirected (ergodic) random graph where we focus on the Barabási-Albert (BA), Erdös-Rényi (ER), and Watts-Strogatz (WS) types. Both walkers and nodes can be either susceptible (S) or infected and infectious (I), representing their state of health. Susceptible nodes may be infected by visits of infected walkers, and susceptible walkers may be infected by visiting infected nodes. No direct transmission of the disease among walkers (or among nodes) is possible. This model mimics a large class of diseases such as Dengue and Malaria with the transmission of the disease via vectors (mosquitoes). Infected walkers may die during the time span of their infection, introducing an additional compartment D of dead walkers. Contrary to the walkers, there is no mortality of infected nodes. Infected nodes always recover from their infection after a random finite time span. This assumption is based on the observation that infectious vectors (mosquitoes) are not ill and do not die from the infection. The infectious time spans of nodes and walkers, and the survival times of infected walkers, are represented by independent random variables. We derive stochastic evolution equations for the mean-field compartmental populations with the mortality of walkers and delayed transitions among the compartments. From linear stability analysis, we derive the basic reproduction numbers RM,R0 with and without mortality, respectively, and prove that RM<R0. For RM,R0>1, the healthy state is unstable, whereas for zero mortality, a stable endemic equilibrium exists (independent of the initial conditions), which we obtained explicitly. We observed that the solutions of the random walk simulations in the considered networks agree well with the mean-field solutions for strongly connected graph topologies, whereas less well for weakly connected structures and for diseases with high mortality. Our model has applications beyond epidemic dynamics, for instance in the kinetics of chemical reactions, the propagation of contaminants, wood fires, and others.

Newborn vaccination game model with potentially periodic behavior

We explore the complex dynamics of epidemics, considering the significant effects of disease transmission, newborn individuals, and mortality rate. Employing an evolutionary game theory approach, we model the vaccination aspect for newborns, incorporating potential periodic behavior. The goal is to create an engaging simulation that underscores the criticality of timely infant vaccinations. By introducing periodic elements, the game adds complexity, fostering player participation and awareness of vaccination schedules. In contrast to traditional intervention game models focused on adult vaccine behavior, our approach recognizes the unique challenges posed by newborn vaccination. We address the limitations of existing models by developing a generalized compartmental model, accommodating infection duration distribution, and accurately capturing both periodic and non-periodic disease trajectories. The results show that higher efficacy in a newborn vaccine program can potentially eradicate the disease, but higher effectiveness and cost may deter vaccination. Increased motivation cost boosts vaccination rates without impacting epidemic size, whereas lower costs stabilize vaccination rates. Lower vaccine costs call for increased government investment to counter hesitancy. However, reduced efficacy and lower motivation lead to higher Vaccine Fear Scores, discouraging participation. Our work also offers a unique perspective on the dilemma of newborn vaccination, providing solutions with closed-form expressions that may exhibit periodic or non-periodic behavior. This approach facilitates disease modelers in exploring the potential periodicity of newborn vaccination programs, aiding efforts to prevent recurrent outbreaks.

Temporal variations in international air travel: implications for modelling the spread of infectious diseases.

The international flight network creates multiple routes by which pathogens can quickly spread across the globe. In the early stages of infectious disease outbreaks, analyses using flight passenger data to identify countries at risk of importing the pathogen are common and can help inform disease control efforts. A challenge faced in this modelling is that the latest aviation statistics (referred to as contemporary data) are typically not immediately available. Therefore, flight patterns from a previous year are often used (referred to as historical data). We explored the suitability of historical data for predicting the spatial spread of emerging epidemics. We analysed monthly flight passenger data from the International Air Transport Association to assess how baseline air travel patterns were affected by outbreaks of Middle East respiratory syndrome (MERS), Zika and severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) over the past decade. We then used a stochastic discrete time susceptible-exposed-infected-recovered (SEIR) metapopulation model to simulate the global spread of different pathogens, comparing how epidemic dynamics differed in simulations based on historical and contemporary data. We observed local, short-term disruptions to air travel from South Korea and Brazil for the MERS and Zika outbreaks we studied, whereas global and longer-term flight disruptions occurred during the SARS-CoV-2 pandemic. For outbreak events that were accompanied by local, small and short-term changes in air travel, epidemic models using historical flight data gave similar projections of the timing and locations of disease spread as when using contemporary flight data. However, historical data were less reliable to model the spread of an atypical outbreak such as SARS-CoV-2, in which there were durable and extensive levels of global travel disruption. The use of historical flight data as a proxy in epidemic models is an acceptable practice, except in rare, large epidemics that lead to substantial disruptions to international travel.

Analyzing the dynamic patterns of COVID-19 through nonstandard finite difference scheme

This paper presents a novel approach to analyzing the dynamics of COVID-19 using nonstandard finite difference (NSFD) schemes. Our model incorporates both asymptomatic and symptomatic infected individuals, allowing for a more comprehensive understanding of the epidemic's spread. We introduce an unconditionally stable NSFD system that eliminates the need for traditional Runge–Kutta methods, ensuring dynamical consistency and numerical accuracy. Through rigorous numerical analysis, we evaluate the performance of different NSFD strategies and validate our analytical findings. Our work demonstrates the benefits of using NSFD schemes for modeling infectious diseases, offering advantages in terms of stability and efficiency. We further illustrate the dynamic behavior of COVID-19 under various conditions using numerical simulations. The results from these simulations demonstrate the effectiveness of the proposed approach in capturing the epidemic's complex dynamics.

Dynamics of a Stochastic SVEIR Epidemic Model with Nonlinear Incidence Rate

This paper delves into the analysis of a stochastic epidemic model known as the susceptible–vaccinated–exposed–infectious–recovered (SVEIR) model, where transmission dynamics are governed by a nonlinear function. In the theoretical analysis section, by suitable stochastic Lyapunov functions, we establish that when the threshold value, denoted as R0s, falls below 1, the epidemic is destined for extinction. Conversely, if the reproduction number R0 of the deterministic model surpasses 1, the model manifests an ergodic endemic stationary distribution. In the numerical simulations and data interpretation section, leveraging a graphical analysis with COVID-19 data, we illustrate that random fluctuations possess the capacity to quell disease outbreaks, underscoring the role of vaccines in curtailing the spread of diseases. This study not only contributes to the understanding of epidemic dynamics but also highlights the pivotal role of stochasticity and vaccination strategies in epidemic control and management. The inherent balance and patterns observed in epidemic spread and control strategies, reflect a symmetrical interplay between stochasticity, vaccination, and disease dynamics.

Study of lump and periodic waves along with rogue waves and breathers for mathematical modeling of biological dynamical system

Globally, infectious diseases pose a significant threat. Notable cases include influenza, Hepatitis B and HIV. COVID-19, caused by the coronavirus, has been the subject of recent discussion due to its great transmissibility. This study explores the Susceptible–Infectious–Recovered (SIR) epidemic model, explaining several analytical approaches to comprehend the nonlinear incident rates and geographic dispersion. The model investigates phenomena such as M-shaped solitons, homoclinic breather-like solitons, lump waves (LWs), lump solution (LS) with one or two kinks, rogue waves (RWs), periodic waves (PWs) and periodic cross-kink waves. These solutions aid in understanding the disease spread and informing containment strategies by identifying optimal outbreak control methods. This work studies localized wave solutions in nonlinear wave equations, known as soliton solutions including the LS. RWs are characterized by unexpectedly large amplitude and rapid profile changes, drawing attention for their erratic features. PWs exhibit periodic repetitions over time and space. Besides, some type of solitons with special waveforms are the periodic cross-kink, M-shaped and homoclinic breather-like solitons. Graphical representation visualizes the behavior of these effective waves, providing insights into virus spread in specific regions over time. SIR models help identify optimal strategies for controlling outbreaks. The work adds to our understanding of epidemic dynamics by illuminating how the movement of susceptible and infected individuals affects the spread of disease.

An outbreak of COVID-19 after a pilgrimage to Medjugorje due to Delta sub-lineages.

A COVID-19 outbreak occurred at the end of October 2021 among pilgrims returning from Medjugorje (Bosnia and Herzegovina). Whole genome sequencing (WGS) of SARS-CoV-2, epidemiological data, and phylogenetic analysis were used to reconstruct outbreak dynamics. The results suggest that only in one case, associated with the SARS-CoV-2 sub-lineage AY.9.2, it is possible to trace back the place of contagion to Medjugorje, while the other cases were likely to be acquired in the country of origin. The combined use of phylogenetic data derived from WGS, and epidemiological data allowed us to study epidemic dynamics and to formulate a possible hypothesis on the place of exposure to SARS-CoV-2. The identification of different sub-lineages of the SARS-CoV-2 Delta variant also suggested that different chains of transmission contributed to the outbreak.