Optimal control and cost effectiveness analysis for Newcastle disease eco-epidemiological model in Tanzania

In this paper, a deterministic compartmental eco- epidemiological model with optimal control of Newcastle disease (ND) in Tanzania is proposed and analysed. Necessary conditions of optimal control problem were rigorously analysed using Pontryagin's maximum principle and the numerical values of model parameters were estimated using maximum likelihood estimator. Three control strategies were incorporated such as chicken vaccination (preventive), human education campaign and treatment of infected human (curative) and its' impact were graphically observed. The incremental cost effectiveness analysis technique used to determine the most cost effectiveness strategy and we observe that combination of chicken vaccination and human education campaign strategy is the best strategy to implement in limited resources. Therefore, ND can be controlled if the farmers will apply chicken vaccination properly and well in time.     

A State Dependent Pulse Control Strategy for a SIRS Epidemic System

With the consideration of mechanism of prevention and control for the spread of infectious diseases, we propose, in this paper, a state dependent pulse vaccination and medication control strategy for a SIRS type epidemic dynamic system. The sufficient conditions on the existence and orbital stability of positive order-1 or order-2 periodic solution are presented. Numerical simulations are carried out to illustrate the main results and compare numerically the state dependent vaccination strategy and the fixed time pulse vaccination strategy.     

Cost-effective control of chronic viral diseases: Finding the optimal level of screening and contact tracing

Chronic viral diseases such as human immunodeficiency virus (HIV) and hepatitis B virus (HBV) afflict millions of people worldwide. A key public health challenge in managing such diseases is identifying infected, asymptomatic individuals so that they can receive antiviral treatment. Such treatment can benefit both the treated individual (by improving quality and length of life) and the population as a whole (through reduced transmission). We develop a compartmental model of a chronic, treatable infectious disease and use it to evaluate the cost and effectiveness of different levels of screening and contact tracing. We show that: (1) the optimal strategy is to get infected individuals into treatment at the maximal rate until the incremental health benefits balance the incremental cost of controlling the disease; (2) as one reduces the disease prevalence by moving people into treatment (which decreases the chance that they will infect others), one should increase the level of contact tracing to compensate for the decreased effectiveness of screening; (3) as the disease becomes less prevalent, it is optimal to spend more per case identified; and (4) the relative mix of screening and contact tracing at any level of disease prevalence is such that the marginal efficiency of contact tracing (cost per infected person found) equals that of screening if possible (e.g., when capacity limitations are not binding). We also show how to determine the cost-effective equilibrium level of disease prevalence (among untreated individuals), and we develop an approximation of the path of the optimal prevalence over time. Using this, one can obtain a close approximation of the optimal solution without having to solve an optimal control problem. We apply our methods to an example of hepatitis B virus.     

Hepatitis B Screening and Vaccination Strategies for Newly Arrived Adult Canadian Immigrants and Refugees: A Cost-Effectiveness Analysis

Background

Immigrants have increased mortality from hepatocellular carcinoma as compared to the host populations, primarily due to undetected chronic hepatitis B virus (HBV) infection. Despite this, there are no systematic programs in most immigrant-receiving countries to screen for chronic HBV infection and immigrants are not routinely offered HBV vaccination outside of the universal childhood vaccination program.

Methods and findings

A cost-effective analysis was performed to compare four HBV screening and vaccination strategies with no intervention in a hypothetical cohort of newly-arriving adult Canadian immigrants. The strategies considered were a) universal vaccination, b) screening for prior immunity and vaccination, c) chronic HBV screening and treatment, and d) combined screening for chronic HBV and prior immunity, treatment and vaccination. The analysis was performed from a societal perspective, using a Markov model. Seroprevalence estimates, annual transition probabilities, health-care costs (in Canadian dollars), and utilities were obtained from the published literature. Acute HBV infection, mortality from chronic HBV, quality-adjusted life years (QALYs), and costs were modeled over the lifetime of the cohort of immigrants. Costs and QALYs were discounted at a rate of 3% per year. Screening for chronic HBV infection, and offering treatment if indicated, was found to be the most cost-effective intervention and was estimated to cost $40,880 per additional QALY gained, relative to no intervention. This strategy was most cost-effective for immigrants < 55 years of age and would cost < $50,000 per additional QALY gained for immigrants from areas where HBV seroprevalence is ≥ 3%. Strategies that included HBV vaccination were either prohibitively expensive or dominated by the chronic HBV screening strategy.

Conclusions

Screening for chronic HBV infection from regions where most Canadian immigrants originate, except for Latin America and the Middle East, was found to be reasonably cost-effective and has the potential to reduce HBV-associated morbidity and mortality.     

带有干扰和非线性指标的脉冲时滞SI模型的渐近性质(英文)

研究了一个带有干扰和非线性指标的脉冲时滞SI模型,通过引入三个引理,获得该疾病最终灭绝和保持持久的充分性条件。结果表明,时滞因素对该模型的全局吸引性和持久性都有影响。此外。如果脉冲免疫接种率的最大值和最小值之比大于某一阈值,则该疾病最终灭绝,本文的主要特点是将多时滞和变系数引入脉冲SI模型,数值模拟表明,该系统具有复杂的动力学行为,包括周期解和周期振荡.     

Can Vaccination Save a Zika Virus Epidemic?

Zika virus (ZIKV) is a vector-borne disease that has rapidly spread during the year 2016 in more than 50 countries around the world. If a woman is infected during pregnancy, the virus can cause severe birth defects and brain damage in their babies. The virus can be transmitted through the bites of infected mosquitoes as well as through direct contact from human to human (e.g., sexual contact and blood transfusions). As an intervention for controlling the spread of the disease, we study a vaccination model for preventing Zika infections. Although there is no formal vaccine for ZIKV, The National Institute of Allergy and Infectious Diseases (part of the National Institutes of Health) has launched a vaccine trial at the beginning of August 2016 to control ZIKV transmission, patients who received the vaccine are expected to return within 44 weeks to determine if the vaccine is safe. Since it is important to understand ZIKV dynamics under vaccination, we formulate a vaccination model for ZIKV spread that includes mosquito as well as sexual transmission. We calculate the basic reproduction number of the model to analyze the impact of relatively, perfect and imperfect vaccination rates. We illustrate several numerical examples of the vaccination model proposed as well as the impact of the basic reproduction numbers of vector and sexual transmission and the effect of vaccination effort on ZIKV spread. Results show that high levels of sexual transmission create larger cases of infection associated with the peak of infected humans arising in a shorter period of time, even when a vaccine is available in the population. However, a high level of transmission of Zika from vectors to humans compared with sexual transmission represents that ZIKV will take longer to invade the population providing a window of opportunities to control its spread, for instance, through vaccination.     

Harnessing Case Isolation and Ring Vaccination to Control Ebola

As a devastating Ebola outbreak in West Africa continues, non-pharmaceutical control measures including contact tracing, quarantine, and case isolation are being implemented. In addition, public health agencies are scaling up efforts to test and deploy candidate vaccines. Given the experimental nature and limited initial supplies of vaccines, a mass vaccination campaign might not be feasible. However, ring vaccination of likely case contacts could provide an effective alternative in distributing the vaccine. To evaluate ring vaccination as a strategy for eliminating Ebola, we developed a pair approximation model of Ebola transmission, parameterized by confirmed incidence data from June 2014 to January 2015 in Liberia and Sierra Leone. Our results suggest that if a combined intervention of case isolation and ring vaccination had been initiated in the early fall of 2014, up to an additional 126 cases in Liberia and 560 cases in Sierra Leone could have been averted beyond case isolation alone. The marginal benefit of ring vaccination is predicted to be greatest in settings where there are more contacts per individual, greater clustering among individuals, when contact tracing has low efficacy or vaccination confers post-exposure protection. In such settings, ring vaccination can avert up to an additional 8% of Ebola cases. Accordingly, ring vaccination is predicted to offer a moderately beneficial supplement to ongoing non-pharmaceutical Ebola control efforts.     

An impulsive delayed SEIRS epidemic model with saturation incidence

A delayed SEIRS epidemic model with pulse vaccination and saturation incidence rate is investigated. Using Krasnoselskii's fixed-point theorem, we obtain the existence of infection-free periodic solution of the impulsive delayed epidemic system. We define some new threshold values R(1), R(2) and R(3). Further, using the comparison theorem, we obtain the explicit formulae of R(1) and R(2). Under the condition R(1) < 1, the infection-free periodic solution is globally attractive, and that R(2) > 1 implies that the disease is permanent. Theoretical results show that the disease will be extinct if the vaccination rate is larger than θ* and the disease is uniformly persistent if the vaccination rate is less than θ(*). Our results indicate that a long latent period of the disease or a large pulse vaccination rate will lead to eradication of the disease. Moreover, we prove that the disease will be permanent as R(3) > 1.     

Optimal Vaccination Policies for an SIR Model with Limited Resources

The purpose of the paper is to use analytical method and optimization tool to suggest a vaccination program intensity for a basic SIR epidemic model with limited resources for vaccination. We show that there are two different scenarios for optimal vaccination strategies, and obtain analytical solutions for the optimal control problem that minimizes the total cost of disease under the assumption of daily vaccine supply being limited. These solutions and their corresponding optimal control policies are derived explicitly in terms of initial conditions, model parameters and resources for vaccination. With sufficient resources, the optimal control strategy is the normal Bang–Bang control. However, with limited resources, the optimal control strategy requires to switch to time-variant vaccination.     

Age-structured non-pharmaceutical interventions for optimal control of COVID-19 epidemic

In an epidemic, individuals can widely differ in the way they spread the infection depending on their age or on the number of days they have been infected for. In the absence of pharmaceutical interventions such as a vaccine or treatment, non-pharmaceutical interventions (e.g. physical or social distancing) are essential to mitigate the pandemic. We develop an original approach to identify the optimal age-stratified control strategy to implement as a function of the time since the onset of the epidemic. This is based on a model with a double continuous structure in terms of host age and time since infection. By applying optimal control theory to this model, we identify a solution that minimizes deaths and costs associated with the implementation of the control strategy itself. We also implement this strategy for three countries with contrasted age distributions (Burkina-Faso, France, and Vietnam). Overall, the optimal strategy varies throughout the epidemic, with a more intense control early on, and depending on host age, with a stronger control for the older population, except in the scenario where the cost associated with the control is low. In the latter scenario, we find strong differences across countries because the control extends to the younger population for France and Vietnam 2 to 3 months after the onset of the epidemic, but not for Burkina Faso. Finally, we show that the optimal control strategy strongly outperforms a constant uniform control exerted over the whole population or over its younger fraction. This improved understanding of the effect of age-based control interventions opens new perspectives for the field, especially for age-based contact tracing.     

Optimizing vaccine allocation at different points in time during an epidemic

Background

Pandemic influenza A(H1N1) 2009 began spreading around the globe in April of 2009 and vaccination started in October of 2009. In most countries, by the time vaccination started, the second wave of pandemic H1N1 2009 was already under way. With limited supplies of vaccine, we are left to question whether it may be a good strategy to vaccinate the high-transmission groups earlier in the epidemic, but it might be a better use of resources to protect instead the high-risk groups later in the epidemic. To answer this question, we develop a deterministic epidemic model with two age-groups (children and adults) and further subdivide each age group in low and high risk.

Methods and Findings

We compare optimal vaccination strategies started at various points in time in two different settings: a population in a developed country where children account for 24% of the population, and a population in a less developed country where children make up the majority of the population, 55%. For each of these populations, we minimize mortality or hospitalizations and we find an optimal vaccination strategy that gives the best vaccine allocation given a starting vaccination time and vaccine coverage level. We find that population structure is an important factor in determining the optimal vaccine distribution. Moreover, the optimal policy is dynamic as there is a switch in the optimal vaccination strategy at some time point just before the peak of the epidemic. For instance, with 25% vaccine coverage, it is better to protect the high-transmission groups before this point, but it is optimal to protect the most vulnerable groups afterward.

Conclusions

Choosing the optimal strategy before or early in the epidemic makes an important difference in minimizing the number of influenza infections, and consequently the number of influenza deaths or hospitalizations, but the optimal strategy makes little difference after the peak.     

On the optimal control of fed-batch reactors with substrate-inhibited kinetics

The optimal feed rate profiles, for fed-batch fermentation that maximizes the biomass production and accounts for time, are analyzed. The solution can be found only if the final arc of the optimal control is a batch arc, since in this case the final concentrations of substrate and biomass can be determined by ulterior conditions on the mass balance and on the final growth rate of biomass and thus it is possible to solve the resulting time optimal problem by using Green's theorem. This evidences the "turnpike property" of the solution, which tries to spend the maximum time on or at least near the singular arc along which the substrate concentration is maintained constant. The optimality of the final batch arc is related to the time operational cost in the performance index. The sequence of the control depends on the initial conditions for which six different regions, with the respective patterns, have been identified, in case the performance index allows the control sequence to have a final batch.     

Vaccination based control of infections in SIRS models with reinfection: special reference to pertussis

The aim of this paper is to study the impact of introducing a partially protective vaccine on the dynamics of infection in SIRS models where primary and secondary infections are distinguished. We investigate whether a public health strategy based solely on vaccinating a proportion of newborns can lead to an effective control of the disease. In addition to carrying out the qualitative analysis, the findings are further explained by numerical simulations. The model exhibits backward bifurcation for certain values of the parameters. In these cases the standard basic reproduction number (obtained by inspection of the uninfected state) is not significant. The key threshold is the reinfection level which depends on the relative transmissibility (susceptibility) of secondary, with respect to primary, infected (susceptible) individuals and the relative loss of immunity of vaccinated, with respect to recovered, individuals. If one or all of these ratios decrease, then the threshold increases which increases the possibility to contain the infection by vaccination. The analysis shows further that symptomatic infections can be eliminated by vaccination solely.     

Effectiveness of realistic vaccination strategies for contact networks of various degree distributions

A "contact network" that models infection transmission comprises nodes (or individuals) that are linked when they are in contact and can potentially transmit an infection. Through analysis and simulation, we studied the influence of the distribution of the number of contacts per node, defined as degree, on infection spreading and its control by vaccination. Three random contact networks of various degree distributions were examined. In a scale-free network, the frequency of high-degree nodes decreases as the power of the degree (the case of the third power is studied here); the decrease is exponential in an exponential network, whereas all nodes have the same degree in a constant network. Aiming for containment at a very early stage of an epidemic, we measured the sustainability of a specific network under a vaccination strategy by employing the critical transmissibility larger than which the epidemic would occur. We examined three vaccination strategies: mass, ring, and acquaintance. Irrespective of the networks, mass preventive vaccination increased the critical transmissibility inversely proportional to the unvaccinated rate of the population. Ring post-outbreak vaccination increased the critical transmissibility inversely proportional to the unvaccinated rate, which is the rate confined to the targeted ring comprising the neighbors of an infected node; however, the total number of vaccinated nodes could mostly be fewer than 100 nodes at the critical transmissibility. In combination, mass and ring vaccinations decreased the pathogen's "effective" transmissibility each by the factor of the unvaccinated rate. The amount of vaccination used in acquaintance preventive vaccination was lesser than the mass vaccination, particularly under a highly heterogeneous degree distribution; however, it was not as less as that used in ring vaccination. Consequently, our results yielded a quantitative assessment of the amount of vaccination necessary for infection containment, which is universally applicable to contact networks of various degree distributions.     

Pulse vaccination strategy in the SIR epidemic model

Theoretical results show that the measles ‘pulse’ vaccination strategy can be distinguished from the conventional strategies in leading to disease eradication at relatively low values of vaccination. Using the SIR epidemic model we showed that under a planned pulse vaccination regime the system converges to a stable solution with the number of infectious individuals equal to zero. We showed that pulse vaccination leads to epidemics eradication if certain conditions regarding the magnitude of vaccination proportion and on the period of the pulses are adhered to. Our theoretical results are confirmed by numerical simulations. The introduction of seasonal variation into the basic SIR model leads to periodic and chaotic dynamics of epidemics. We showed that under seasonal variation, in spite of the complex dynamics of the system, pulse vaccination still leads to epidemic eradication. We derived the conditions for epidemic eradication under various constraints and showed their dependence on the parameters of the epidemic. We compared effectiveness and cost of constant, pulse and mixed vaccination policies.     

一类具有饱和反应率的脉冲免疫接种的SIS模型

研究了具饱和传染率的脉冲免疫接种SIS模型,得到了无病周期解全局渐近稳定的充分条件和系统持续生存的充分条件．     

Social life factors affecting the mortality, longevity, and birth rate of total Japanese population: effects of rapid industrialization and urbanization

To expand upon the findings that lower mortality was found in Japanese urban areas in contrast to the Western model where in the US and Britain the risk of death was higher in metropolitan areas and conurbations, 22 social life indicators are examined among 46 prefectures in Japan in terms of their effect on age specific mortality, life expectancy, and age adjusted marriage, divorce, and birth rates. The effects of these factors on age adjusted mortality for 8 major working and nonworking male populations, where also analyzed. The 22 social life factors were selected from among 227 indicators in the system of Statistical Indicators on Life. Factor analysis was used to classify the indicators into 8 groups of factors for 1970 and 7 for 1975. Factors 1-3 for both years were rural or urban residence, low income and unemployment, and prefectural age distribution. The 4th for 1970 was home help for the elderly and for 1975, social mobility. The social life indicators were classified form 1 to 8 as rural residence in 1970 and 1975, urban residence, low income, high employment, old age, young age, social mobility, and home help for the elderly which moved from 8th place in 1970 to 1st in 1975. Between 1960-75, rapid urbanization took place with the proportion of farmers, fishermen, and workers declining from 43% in 1960 to 19% in 1975. The results of stepwise regression analysis indicate a positive relationship of urban residence with mortality of men and women except school-aged and middle-aged women, and the working populations, as well as life expectancy at birth for males and females and ages 20 and 40 years for males. Rural residence was positively associated with the male marriage rate, whereas the marriage rate for females was affected by industrialization and urbanization. High employment and social mobility were positively related to the female marriage rate. Low income was positively related to the divorce rate for males and females. Rural residence and high employment were positively related to the birth rate. The birth rate is higher in rural areas. Mortality of professional, engineering, and administrative workers was slightly lower than the total working population, while sales workers, those in farming, fishing, and forestry, and in personal and domestic service had significantly higher mortality. The mortality of the nonworking population was 6-8 times higher than sales, transportation, and communication, and personal and domestic service as well as the total population.     

Optimal control of epidemics with limited resources

We extend the existing work on the time-optimal control of the basic SIR epidemic model with mass action contact rate. Previous results have focused on minimizing an objective function that is a linear combination of the cost associated with using control and either the outbreak size or the infectious burden. We instead, provide analytic solutions for the control that minimizes the outbreak size (or infectious burden) under the assumption that there are limited control resources. We provide optimal control policies for an isolation only model, a vaccination only model and a combined isolation–vaccination model (or mixed model). The optimal policies described here contain many interesting features especially when compared to previous analyses. For example, under certain circumstances the optimal isolation only policy is not unique. Furthermore the optimal mixed policy is not simply a combination of the optimal isolation only policy and the optimal vaccination only policy. The results presented here also highlight a number of areas that warrant further study and emphasize that time-optimal control of the basic SIR model is still not fully understood.     

An SIRVS epidemic model with pulse vaccination strategy

The aim of this paper is to analyze an SIRVS epidemic model in which pulse vaccination strategy (PVS) is included. We are interested in finding the basic reproductive number of the model which determine whether or not the disease dies out. The global attractivity of the disease-free periodic solution (DFPS for short) is obtained when the basic reproductive number is less than unity. The disease is permanent when the basic reproductive number is greater than unity, i.e., the epidemic will turn out to endemic. Our results indicate that the disease will go to extinction when the vaccination rate reaches some critical value.     

An optimizing start-up strategy for a bio-methanator

This paper presents an optimizing start-up strategy for a bio-methanator. The goal of the control strategy is to maximize the outflow rate of methane in anaerobic digestion processes, which can be described by a two-population model. The methodology relies on a thorough analysis of the system dynamics and involves the solution of two optimization problems: steady-state optimization for determining the optimal operating point and transient optimization. The latter is a classical optimal control problem, which can be solved using the maximum principle of Pontryagin. The proposed control law is of the bang–bang type. The process is driven from an initial state to a small neighborhood of the optimal steady state by switching the manipulated variable (dilution rate) from the minimum to the maximum value at a certain time instant. Then the dilution rate is set to the optimal value and the system settles down in the optimal steady state. This control law ensures the convergence of the system to the optimal steady state and substantially increases its stability region. The region of attraction of the steady state corresponding to maximum production of methane is considerably enlarged. In some cases, which are related to the possibility of selecting the minimum dilution rate below a certain level, the stability region of the optimal steady state equals the interior of the state space. Aside its efficiency, which is evaluated not only in terms of biogas production but also from the perspective of treatment of the organic load, the strategy is also characterized by simplicity, being thus appropriate for implementation in real-life systems. Another important advantage is its generality: this technique may be applied to any anaerobic digestion process, for which the acidogenesis and methanogenesis are, respectively, characterized by Monod and Haldane kinetics.