Hepatitis C is a viral infection that appears as a result of the Hepatitis C Virus (HCV), and it has been recognized as the main reason for liver diseases. HCV incidence is growing as an important issue in the epidemiology of infectious diseases. In the present study, a mathematical model is employed for simulating the dynamics of HCV outbreak in a population. The total population is divided into five compartments, including unaware and aware susceptible, acutely and chronically infected, and treated classes. Then, a Lyapunov-based nonlinear adaptive method is proposed for the first time to control the HCV epidemic considering modelling uncertainties. A positive definite Lyapunov candidate function is suggested, and adaptation and control laws are attained based on that. The main goal of the proposed control strategy is to decrease the population of unaware susceptible and chronically infected compartments by pursuing appropriate treatment scenarios. As a consequence of this decrease in the mentioned compartments, the population of aware susceptible individuals increases and the population of acutely infected and treated humans decreases. The Lyapunov stability theorem and Barbalat's lemma are employed in order to prove the tracking convergence to desired population reduction scenarios. Based on the acquired numerical results, the proposed nonlinear adaptive controller can achieve the above-mentioned objective by adjusting the inputs (rates of informing the susceptible people and treatment of chronically infected ones) and estimating uncertain parameter values based on the designed control and adaptation laws, respectively. Moreover, the proposed strategy is designed to be robust in the presence of different levels of parametric uncertainties.
In this paper, we present the global analysis of a HCV model under therapy. We prove that the solutions with positive initial values are global, positive, bounded and not display periodic orbits. In addition, we show that the model is globally asymptotically stable, by using appropriate Lyapunov functions.
The aims of this work is to analyse of the global stability of the extended model of hepatitis C virus(HCV) infection with cellular proliferation, spontaneous cure and hepatocyte homeostasis. We first give general information about hepatitis C. Secondly, We prove the existence of local, maximal and global solutions of the model and establish some properties of this solution as positivity and asymptotic behaviour. Thirdly we show, by the construction of an appropriate Lyapunov function, that the uninfected equilibrium and the unique infected equilibrium of the model of HCV are globally asymptot…
This paper considers a mathematical model based on the transmission dynamics of hepatitis C virus (HCV) infection. In addition to the usual compartments for susceptible, exposed, and infected individuals, this model includes compartments for individuals who are under treatment and those who have had vaccination against HCV infection. It is assumed that the immunity provided by the vaccine fades with time. The basic reproduction number, $R_0$, and the equilibrium solutions of the model are determined. The model exhibits the phenomenon of backward bifurcation where a stable disease-free equilibr…
In this paper, a mathematical analysis of the global dynamics of a viral infection model in vivo is carried out. We study the dynamics of a hepatitis C virus (HCV) model, under therapy, that considers both extracellular and intracellular levels of infection. At present most mathematical modeling of viral kinetics after treatment only addresses the process of infection of a cell by the virus and the release of virions by the cell, while the processes taking place inside the cell are not included. We prove that the solutions of the new model with positive initial values are positive, exist globa…
We define and examine a model of epidemic propagation for a virus such as Hepatitis C (with HIV co-infection) on a network of networks, namely the network of French urban areas. One network level is that of the individual interactions inside each urban area. The second level is that of the areas themselves, linked by individuals travelling between these areas and potentially helping the epidemic spread from one city to another. We choose to encode the second level of the network as extra, special nodes in the first level. We observe that such an encoding leads to sensible results in terms of t…
The scope of this work is to serve as a guiding tool against subjective estimations on real pandemic situations (mainly due to the inability to acquire objective real data over whole populations). The previously introduced model of closed self-organized criticality (SOC), is adapted in the case of a virus-induced epidemic. In this version this physical model can distinguish the virus spread according to the virus aggressiveness. The study presented, highlights the critical value of virus density over a population. For low values of the initial virus density (lower than the critical value) it i…
A system of 4 nonlinearly-coupled Ordinary Differential Equations has been recently introduced to investigate the evolution of human respiratory virus epidemics. In this paper we point out that some explicit solutions of that system can be obtained by algebraic operations, provided the parameters of the model satisfy certain constraints.
During a long-running pandemic a pathogen can mutate, producing new strains with different epidemiological parameters. Existing approaches to epidemic modelling only consider one virus strain. We have developed a modified SEIR model to simulate multiple virus strains within the same population. As a case study, we investigate the potential effects of SARS-CoV-2 strain B.1.1.7 on the city of Moscow. Our analysis indicates a high risk of a new wave of infections in September-October 2021 with up to 35 000 daily infections at peak. We open-source our code and data.
In this paper we study some deterministic mathematical models that seek to explain the expansion of zika virus, as a viral epidemic, using published data for Brazil. SIR type models are proposed and validated using the epidemic data found, considering several aspects in the spread of the disease. Finally, we confirmed that the crucial epidemic parameter such as $R_0$ is consistent with those previously reported in the literature for other areas. We also explored variations of the parameters within Brazil for different federal entities. We concluded that a parsimonious model that includes both …
Simultaneous reconstruction of evolutionary history and epidemiological dynamics from viral sequences with the birth-death SIR model
RNA病毒如HIV、丙型肝炎病毒和流感病毒的进化如此之快，以至于病毒的基因组包含了过去生态动态的信息。因此，我们开发了一种动态的方法，使联合估计的流行病学参数和系统发育史。该方法基于房室易感染-感染-清除（SIR）模型，提供了关于感染发生率和患病率的单独信息。关于宿主种群动力学和进化历史相互作用的详细信息可以为如何控制或完全避免疾病爆发的决策提供信息。我们应用我们的死亡SIR方法（BDSIR）的两个病毒数据集。首先，分析了1999年至2003年期间在英国采样的5个人类免疫缺陷病毒1型簇。估计的基本繁殖比在集群之间的范围从1.9到3.2。所有集群都显示，在90年代中期或末期，当地流行病的增长率有所下降。对丙型肝炎病毒（HCV）基因型2c数据集的分析表明，科尔多瓦市Cruz del Eje的当地流行病起源于1906年左右（中位数），与1880- 1920年从欧洲到阿根廷中部的移民潮相吻合。估计流行高峰期在1970年左右。
We investigate a stochastic individual-based model for the population dynamics of host-virus systems where the microbial hosts may transition into a dormant state upon contact with virions, thus evading infection. Such a contact-mediated defence mechanism was described in Bautista et al (2015) for an archaeal host, while Jackson and Fineran (2019) and Meeske et al (2019) describe a related, CRISPR-Cas induced, dormancy defense of bacterial hosts to curb phage epidemics. We first analyse the effect of the dormancy-related model parameters on the probability and time of invasion of a newly arriv…
In this paper, we carry out a computational study using the spectral decomposition of the fluctuations of a two-pathogen epidemic model around its deterministic attractor, i.e., steady state or limit cycle, to examine the role of partial vaccination and between-host pathogen interaction on early pathogen replacement during seasonal epidemics of influenza and respiratory syncytial virus.
The dynamics of the spread of contagions such as viruses, infectious diseases or even rumors/opinions over contact networks (graphs) have effectively been captured by the well known \textit{Susceptible-Infected-Susceptible} ($SIS$) epidemic model in recent years. When it comes to competition between two such contagions spreading on overlaid graphs, their propagation is captured by so-called \textit{bi-virus} epidemic models. Analysis of such dynamical systems involve the identification of equilibrium points and its convergence properties, which determine whether either of the viruses dies out,…
Containing the recent West African outbreak of Ebola virus (EBOV) required the deployment of substantial global resources. Operationally, health workers and surveillance teams treated cases, collected genetic samples, and tracked case contacts. Despite the substantial progress in analyzing and modeling EBOV epidemiological data, a complete characterization of the spatiotemporal spread of Ebola cases remains a challenge. In this work, we offer a novel perspective on the EBOV epidemic that utilizes virus genome sequences to inform population-level, spatial models. Calibrated to phylogenetic link…
Background: While RSV circulation results in high burden of hospitalization, particularly among infants, young children and the elderly, little is known about the role of different age groups in propagating annual RSV epidemics in the community. Methods: During a communicable disease outbreak, some subpopulations may play a disproportionate role during the outbreak's ascent due to increased susceptibility and/or contact rates. Such subpopulations can be identified by considering the proportion that cases in a subpopulation represent among all cases in the population occurring before (Bp) and a…
Multiple instances of Zika virus epidemic have been reported around the world in the last two decades, turning the related illness into an international concern. In this context the use of mathematical models for epidemics is of great importance, since they are useful tools to study the underlying outbreak numbers and allow one to test the effectiveness of different strategies used to combat the associated diseases. This work deals with the development and calibration of an epidemic model to describe the 2016 outbreak of Zika virus in Brazil. A system of 8 differential equations with 8 paramet…
A human respiratory syncytial virus surveillance system was implemented in Florida in 1999, to support clinical decision-making for prophylaxis of premature newborns. Recently, a local periodic SEIRS mathematical model was proposed in [Stat. Optim. Inf. Comput. 6 (2018), no.1, 139--149] to describe real data collected by Florida's system. In contrast, here we propose a non-local fractional (non-integer) order model. A fractional optimal control problem is then formulated and solved, having treatment as the control. Finally, a cost-effectiveness analysis is carried out to evaluate the cost and …
Theoretical modeling of computer virus/worm epidemic dynamics is an important problem that has attracted many studies. However, most existing models are adapted from biological epidemic ones. Although biological epidemic models can certainly be adapted to capture some computer virus spreading scenarios (especially when the so-called homogeneity assumption holds), the problem of computer virus spreading is not well understood because it has many important perspectives that are not necessarily accommodated in the biological epidemic models. In this paper we initiate the study of such a perspecti…
Vector-transmitted diseases such as dengue fever and chikungunya have been spreading rapidly in many parts of the world. The Zika virus has been known since 1947 and invaded South America in 2013. It can be transmitted not only by (mosquito) vectors but also directly through sexual contact. Zika has developed into a serious global health problem because, while most cases are asymptomatic or very light, babies born to Zika - infected mothers may develop microcephaly and other very serious birth defects. We formulate and analyze two epidemic models for vector-transmitted diseases, one appropriat…
The role of transportation vehicles, pig movement between farms, proximity to infected premises, and feed deliveries has not been fully considered in the dissemination dynamics of porcine epidemic diarrhea virus (PEDV). This has limited efforts for disease control and elimination restricting the development of risk-based resource allocation to the most relevant modes of PEDV dissemination. Here, we modeled nine modes of between-farm transmission pathways including farm-to-farm proximity (local transmission), contact network of pig farm movements between sites, four different contact networks o…
At the moment of writing (12 February, 2020), the future evolution of the 2019-nCoV virus is unclear. Predictions of the further course of the epidemic are decisive to deploy targeted disease control measures. We consider a network-based model to describe the 2019-nCoV epidemic in the Hubei province. The network is composed of the cities in Hubei and their interactions (e.g., traffic flow). However, the precise interactions between cities is unknown and must be inferred from observing the epidemic. We propose a network-based method to predict the future prevalence of the 2019-nCoV virus in eve…
Rapid antigen tests detect proteins at the surface of virus particles, identifying the disease during its infectious phase. In contrast, PCR tests detect viral genomes; they can thus diagnose COVID-19 before the infectious phase but also react to remnants of the virus genome, even weeks after live virus ceases to be detectable in the respiratory tract. Furthermore, the logistics for administering the tests are different, with rapid antigen tests being much easier to administer at-scale. In this article, we discuss the relative advantages of the different testing procedures and summarise eviden…
As of October 12, 2018, 211 cases of Ebola virus disease (EVD) were reported in North Kivu Province, Democratic Republic of Congo. Since the beginning of October the outbreak has largely shifted into regions in which active armed conflict is occurring, and in which EVD cases and their contacts are difficult for health workers to reach. We modeled EVD transmission using a branching process with gradually quenching transmission estimated from past EVD outbreaks, with outbreak trajectories conditioned on agreement with the course of the current outbreak, and with multiple levels of vaccination co…
Be-CoDiS: A mathematical model to predict the risk of human diseases spread between countries. Validation and application to the 2014-15 Ebola Virus Disease epidemic
Hepatitis C virus (HCV) infection is endemic in people who inject drugs (PWID), with prevalence estimates above 60 percent for PWID in the United States. Previous modeling studies suggest that direct acting antiviral (DAA) treatment can lower overall prevalence in this population, but treatment is often delayed until the onset of advanced liver disease (fibrosis stage 3 or later) due to cost. Lower cost interventions featuring syringe access (SA) and medically assisted treatment (MAT) for addiction are known to be less costly, but have shown mixed results in lowering HCV rates below current le…
The COVID-19 (formerly, 2019-nCoV) epidemic has become a global health emergency, as such, WHO declared PHEIC. China has taken the most hit since the outbreak of the virus, which could be dated as far back as late November by some experts. It was not until January 23rd that the Wuhan government finally recognized the severity of the epidemic and took a drastic measure to curtain the virus spread by closing down all transportation connecting the outside world. In this study, we seek to answer a few questions: How did the virus get spread from the epicenter Wuhan city to the rest of the country?…
We introduce and investigate an SIS-type model for the spread of an infectious disease, where the infected population is structured with respect to the different strain of the virus/bacteria they are carrying. Our aim is to capture the interesting scenario when individuals infected with different strains cause secondary (new) infections at different rates. Therefore, we consider a nonlinear infection process, which generalises the bilinear process arising from the classic mass-action assumption. Our main motivation is to study competition between different strains of a virus/bacteria. From the…
The novel coronavirus disease (COVID-19) is known as the causative virus of outbreak pneumonia initially recognized in the mainland of China, late December 2019. COVID-19 reaches out to many countries in the world, and the number of daily cases continues to increase rapidly. In order to simulate, track, and forecast the trend of the virus spread, several mathematical and statistical models have been developed. Susceptible-Exposed-Infected-Quarantined-Recovered-Death-Insusceptible (SEIQRDP) model is one of the most promising dynamic systems that has been proposed for estimating the transmissibi…
In the article a virus transmission model is constructed on a simplified social network. The social network consists of more than 2 million nodes, each representing an inhabitant of Slovenia. The nodes are organised and interconnected according to the real household and elderly-care center distribution, while their connections outside these clusters are semi-randomly distributed and fully-linked. The virus spread model is coupled to the disease progression model. The ensemble approach with the perturbed transmission and disease parameters is used to quantify the ensemble spread, a proxy for th…
The June software package is an open-source framework for the detailed simulation of epidemics based on social interactions in a virtual population reflecting age, gender, ethnicity, and socio-economic indicators in England. In this paper, we present a new version of the framework specifically adapted for Germany, which allows the simulation of the entire German population using publicly available information on households, schools, universities, workplaces, and mobility data for Germany. Moreover, JuneGermany incorporates testing and vaccination strategies within the population as well as the…
Intuitively, sampling is likely to be more efficient for prevalence estimation, if the cases (or positives) have a relatively higher representation in the sample than in the population. In case the virus is transmitted via personal contacts, contact tracing of the observed cases (but not noncases), to be referred to as \emph{adaptive network tracing}, can generate a higher yield of cases than random sampling from the population. The efficacy of relevant designs for cross-sectional and change estimation is investigated. The availability of these designs allows one unite tracing for combating th…
After the blockade that many nations suffered to stop the growth of the incidence curve of COVID-19 during the first half of 2020, they face the challenge of resuming their social and economic activity. The rapid airborne transmissibility of SARS-CoV-2, and the absence of a vaccine, calls for active containment measures to avoid the propagation of transmission chains. The best strategy up to date, popularly known as Test-Track-Treat (TTT), consist in testing the population for diagnosis, track the contacts of those infected, and treat by quarantine all these cases. The dynamical process that b…
There were 27 novel coronavirus pneumonia cases found in Wuhan, China in December 2019, named as 2019-nCoV temporarily and COVID-19 formally by WHO on 11 February, 2020. In December 2019 and January 2020, COVID-19 has spread in large scale among the population, which brought terrible disaster to the life and property of the Chinese people. In this paper, we will first analyze the feature and pattern of the virus transmission, and discuss the key impact factors and uncontrollable factors of epidemic transmission based on public data. Then the virus transmission can be modelled and used for the …
A state wide Human Respiratory Syncytial Virus (HRSV) surveillance system was implemented in Florida in 1999 to support clinical decision-making for prophylaxis of premature infants. The research presented in this paper addresses the problem of fitting real data collected by the Florida HRSV surveillance system by using a periodic SEIRS mathematical model. A sensitivity and cost-effectiveness analysis of the model is done and an optimal control problem is formulated and solved with treatment as the control variable.
