Analysis, Simulation and Control of a New Measles Epidemic Model

In this paper the problem of modeling and controlling the measles epidemic spread is faced. A new model is proposed and analysed; besides the categories usually considered in measles modeling, the susceptible, the exposed, the infected, the removed and, less frequently, the quarantine individuals, two new categories are herein introduced: the immunosuppressed subjects, that can not be vaccinated, and the patients with an additional complication, not risky by itself but dangerous if caught togeter with the measles. These two novelties are taken into account in designing and scheduling suitably control actions such as vaccination, whenever possible, prevention, quarantine and treatment, when limited resources are available. An analysis of the model is developed and the optimal control strategies are compared with other not optimized actions. By using the Pontryagin principle, it is shown the prevailing role of the vaccination in guaranteeing the protection to immunosuppressed individuals, as well as the importance of a prompt response of the society when an epidemic spread occurs, such as the quarantine intervention

Modeling, analysis and defense strategies against Internet attacks.

Third, we have analyzed the tradeoff between delay caused by filtering of worms at routers, and the delay due to worms' excessive amount of network traffic. We have used the optimal control problem, to determine the appropriate tradeoffs between these two delays for a given rate of a worm spreading. Using our technique we can minimize the overall network delay by finding the number of routers that should perform filtering and the time at which they should start the filtering process.Many early Internet protocols were designed without a fundamentally secure infrastructure and hence vulnerable to attacks such as denial of service (DoS) attacks and worms. DoS attacks attempt to consume the resources of a remote host or network, thereby denying or degrading service to legitimate users. Network forensics is an emerging area wherein the source or the cause of the attacker is determined using IDS tools. The problem of finding the source(s) of attack(s) is called the "trace back problem". Lately, Internet worms have become a major problem for the security of computer networks, causing considerable amount of resources and time to be spent recovering from the disruption of systems. In addition to breaking down victims, these worms create large amounts of unnecessary network data traffic that results in network congestion, thereby affecting the entire network.In this dissertation, first we solve the trace back problem more efficiently in terms of the number of routers needed to complete the track back. We provide an efficient algorithm to decompose a network into connected components and construct a terminal network. We show that for a terminal network with n routers, the trace back can be completed in O(log n) steps.Second, we apply two classical epidemic SIS and SIR models to study the spread of Internet Worm. The analytical models that we provide are useful in determining the rate of spread and time required to infect a majority of the nodes in the network. Our simulation results on large Internet like topologies show that in a fairly small amount of time, 80% of the network nodes is infected

An Sveir Model for Assessing Potential Impact of an Imperfect Anti-SARS Vaccine

The control of severe acute respiratory syndrome (SARS), a fatal contagious viral disease that spread to over 32 countries in 2003, was based on quarantine of latently infected individuals and isolation of individuals with clinical symptoms of SARS. Owing to the recent ongoing clinical trials of some candidate anti-SARS vaccines, this study aims to assess, via mathematical modelling, the potential impact of a SARS vaccine, assumed to be imperfect, in curtailing future outbreaks. A relatively simple deterministic model is designed for this purpose. It is shown, using Lyapunov function theory and the theory of compound matrices, that the dynamics of the model are determined by a certain threshold quantity known as the control reproduction number (Rv). If Rv ≤ 1, the disease will be eliminated from the community; whereas an epidemic occurs if Rv \u3e 1. This study further shows that an imperfect SARS vaccine with infection-blocking efficacy is always beneficial in reducing disease spread within the community, although its overall impact increases with increasing efficacy and coverage. In particular, it is shown that the fraction of individuals vaccinated at steady-state and vaccine efficacy play equal roles in reducing disease burden, and the vaccine must have efficacy of at least 75% to lead to effective control of SARS (assuming R0 = 4). Numerical simulations are used to explore the severity of outbreaks when Rv \u3e 1

Simulation modeling of zoonotic diseases between swine and human populations for informing policy decisions

Approximately 60% of human pathogens and emerging infectious diseases are zoonotic. Simulation models are increasingly being used to investigate the spread of diseases, evaluate intervention strategies and guide the decisions of policy makers. In this thesis a systematic review of modeling methods and approaches used for zoonotic influenza in animals and humans was conducted, and knowledge gaps were identified. Furthermore, the disease spread and intervention parameters used in these studies were summarized for ready reference in future work. Building on this review work, the research presented in this thesis evaluated the effects of transmissibility of the pandemic H1N1 2009 (pH1N1) virus at the swine- human interface and the control strategies against its spread in swine and human populations as a case study for zoonotic disease modeling. The feasibility of North American Animal Disease Spread Model (NAADSM) for modeling directly transmitted zoonoses was also assessed. Population data based on swine herds and households (categorized as rural households with or without swine workers, and urban households without swine workers) of a county in Ontario, Canada was used. The swine workers served as a bridging population for the spread of the virus between swine herds and households. Scenarios based on the combinations of the transmissibility of the virus (low (L), medium (M), and high (H)) from swine-to-human and human-to-swine (LL, ML, HL, MM, HM, LL), and targeted vaccination of swine worker households (0% to 60%) were evaluated. The results showed that lowering the influenza transmissibility at the interface to low level and providing higher vaccine coverage (60%) had significant beneficial effects on all outcome measures. However, these measures had little or negligible impact on the total number of rural and urban households infected. A set of models evaluating the combination of control strategies indicated that a moderate speed of the detection (within 5 to 10 days of the first infection), combined with the quarantine of detected units alone, contained the outbreak within the swine population in most simulations. However, a zone-based quarantine strategy was more effective when the detection was delayed until around three weeks after initial infection. Ring vaccination had no added beneficial effect. This work suggested that NAADSM can be used for modeling the directly transmitted zoonotic diseases under similar simplifying assumptions adopted in these studies. However, this needs to be evaluated further with more accurate parameters and influenza outbreak data. To fill in some of the gaps identified in the review study, network analyses of swine shipments among farms, and between farms and abattoirs were conducted. This provided network metrics and parameters necessary for disease modeling and risk-based disease management in swine in Ontario for the first time. Finally, agent-based network models assessing the spread and control of pH1N1 in swine established the importance of explicitly incorporating appropriate contact network structures into such models to increase their validity. It also demonstrated the benefits of targeted control strategies against highly connected farms. In conclusion, the modeling tools developed in this thesis can assist decision makers in preparedness and response of outbreaks of infectious diseases as more information become available for the parameterization of models

Evaluation of the effect of different policies in the containment of epidemic spreads for the COVID-19 case

The paper presents a new mathematical model for the SARS-CoV-2 virus propagation, designed to include all the possible actions to prevent the spread and to help in the healing of infected people. After a discussion on the equilibrium and stability properties of the model, the effects of each different control actions on the evolution of the epidemic spread are analysed, through numerical evaluations for a more intuitive and immediate presentation, showing the consequences on the classes of the population

COVID-19 pandemic control: balancing detection policy and lockdown intervention under ICU sustainability

We consider here an extended SIR model, including several features of the recent COVID-19 outbreak: in particular the infected and recovered individuals can either be detected (+) or undetected (-) and we also integrate an intensive care unit (ICU) capacity. Our model enables a tractable quantitative analysis of the optimal policy for the control of the epidemic dynamics using both lockdown and detection intervention levers. With parametric specification based on literature on COVID-19, we investigate the sensitivities of various quantities on the optimal strategies, taking into account the subtle trade-off between the sanitary and the socio-economic cost of the pandemic, together with the limited capacity level of ICU. We identify the optimal lockdown policy as an intervention structured in 4 successive phases: First a quick and strong lockdown intervention to stop the exponential growth of the contagion; second a short transition phase to reduce the prevalence of the virus; third a long period with full ICU capacity and stable virus prevalence; finally a return to normal social interactions with disappearance of the virus. The optimal scenario hereby avoids the second wave of infection, provided the lockdown is released sufficiently slowly. We also provide optimal intervention measures with increasing ICU capacity, as well as optimization over the effort on detection of infectious and immune individuals. Whenever massive resources are introduced to detect infected individuals, the pressure on social distancing can be released, whereas the impact of detection of immune individuals reveals to be more moderate

Extracting key information from historical data to quantify the transmission dynamics of smallpox

<p>Abstract</p> <p>Background</p> <p>Quantification of the transmission dynamics of smallpox is crucial for optimizing intervention strategies in the event of a bioterrorist attack. This article reviews basic methods and findings in mathematical and statistical studies of smallpox which estimate key transmission parameters from historical data.</p> <p>Main findings</p> <p>First, critically important aspects in extracting key information from historical data are briefly summarized. We mention different sources of heterogeneity and potential pitfalls in utilizing historical records. Second, we discuss how smallpox spreads in the absence of interventions and how the optimal timing of quarantine and isolation measures can be determined. Case studies demonstrate the following. (1) The upper confidence limit of the 99th percentile of the incubation period is 22.2 days, suggesting that quarantine should last 23 days. (2) The highest frequency (61.8%) of secondary transmissions occurs 3–5 days after onset of fever so that infected individuals should be isolated before the appearance of rash. (3) The U-shaped age-specific case fatality implies a vulnerability of infants and elderly among non-immune individuals. Estimates of the transmission potential are subsequently reviewed, followed by an assessment of vaccination effects and of the expected effectiveness of interventions.</p> <p>Conclusion</p> <p>Current debates on bio-terrorism preparedness indicate that public health decision making must account for the complex interplay and balance between vaccination strategies and other public health measures (e.g. case isolation and contact tracing) taking into account the frequency of adverse events to vaccination. In this review, we summarize what has already been clarified and point out needs to analyze previous smallpox outbreaks systematically.</p