Optimal control strategy for prevention of avian influenza pandemic

Optimal social distancing in epidemic control: cost prioritization, adherence and insights into preparedness principles

The COVID-19 pandemic experience has highlighted the importance of developing general control principles to inform future pandemic preparedness based on the tension between the different control options, ranging from elimination to mitigation, and related costs. Similarly, during the COVID-19 pandemic, social distancing has been confirmed to be the critical response tool until vaccines become available. Open-loop optimal control of a transmission model for COVID-19 in one of its most aggressive outbreaks is used to identify the best social distancing policies aimed at balancing the direct epidemiological costs of a threatening epidemic with its indirect (i.e., societal level) costs arising from enduring control measures. In particular, we analyse how optimal social distancing varies according to three key policy factors, namely, the degree of prioritization of indirect costs, the adherence to control measures, and the timeliness of intervention. As the prioritization of indirect costs increases, (i) the corresponding optimal distancing policy suddenly switches from elimination to suppression and, finally, to mitigation; (ii) the "effective" mitigation region-where hospitals' overwhelming is prevented-is dramatically narrow and shows multiple control waves; and (iii) a delicate balance emerges, whereby low adherence and lack of timeliness inevitably force ineffective mitigation as the only accessible policy option. The present results show the importance of open-loop optimal control, which is traditionally absent in public health preparedness, for studying the suppression-mitigation trade-off and supplying robust preparedness guidelines.

Reframing Optimal Control Problems for Infectious Disease Management in Low-Income Countries

Optimal control theory can be a useful tool to identify the best strategies for the management of infectious diseases. In most of the applications to disease control with ordinary differential equations, the objective functional to be optimized is formulated in monetary terms as the sum of intervention costs and the cost associated with the burden of disease. We present alternate formulations that express epidemiological outcomes via health metrics and reframe the problem to include features such as budget constraints and epidemiological targets. These alternate formulations are illustrated with a compartmental cholera model. The alternate formulations permit us to better explore the sensitivity of the optimal control solutions to changes in available budget or the desired epidemiological target. We also discuss some limitations of comprehensive cost assessment in epidemiology.

Analyzing factors contributing to COVID-19 mortality in the United States using artificial intelligence techniques

Having started since late 2019, COVID-19 has spread through far many nations around the globe. Not being known profoundly, the novel virus of the Coronaviruses family has already caused more than half a million deaths and put the lives of many more people in danger. Policymakers have implemented preventive measures to curb the outbreak of the virus, and health practitioners along with epidemiologists have pointed out many social and hygienic factors associated with the virus incidence and mortality. However, a clearer vision of how the various factors cited hitherto can affect total death in different communities is yet to be analyzed. This study has put this issue forward. Applying artificial intelligence techniques, the relationship between COVID-19 death toll and determinants mentioned as strongly influential in earlier studies was investigated. In the first stage, employing Best-Worst Method, the weight of the primer contributing factor, effectiveness of strategies, was estimated. Then, using an integrated Best-Worst Method-local linear neuro-fuzzy-adaptive neuro-fuzzy inference system approach, the relationship between COVID-19 mortality rate and all factors namely effectiveness of strategies, age pyramid, health system status, and community health status was elucidated more specifically.

Nonlinear optimal control strategies for a mathematical model of COVID-19 and influenza co-infection

Infectious diseases have remained one of humanity's biggest problems for decades. Multiple disease infections, in particular, have been shown to increase the difficulty of diagnosing and treating infected people, resulting in worsening human health. For example, the presence of influenza in the population is exacerbating the ongoing COVID-19 pandemic. We formulate and analyze a deterministic mathematical model that incorporates the biological dynamics of COVID-19 and influenza to effectively investigate the co-dynamics of the two diseases in the public. The existence and stability of the disease-free equilibrium of COVID-19-only and influenza-only sub-models are established by using their respective threshold quantities. The result shows that the COVID-19 free equilibrium is locally asymptotically stable whenR C < 1 , whereas the influenza-only model, is locally asymptotically stable whenR F < 1 . Furthermore, the existence of the endemic equilibria of the sub-models is examined while the conditions for the phenomenon of backward bifurcation are presented. A generalized analytical result of the COVID-19-influenza co-infection model is presented. We run a numerical simulation on the model without optimal control to see how competitive outcomes between-hosts and within-hosts affect disease co-dynamics. The findings established that disease competitive dynamics in the population are determined by transmission probabilities and threshold quantities. To obtain the optimal control problem, we extend the formulated model by including three time-dependent control functions. The maximum principle of Pontryagin was used to prove the existence of the optimal control problem and to derive the necessary conditions for optimum disease control. A numerical simulation was performed to demonstrate the impact of different combinations of control strategies on the infected population. The findings show that, while single and twofold control interventions can be used to reduce disease, the threefold control intervention, which incorporates all three controls, will be the most effective in reducing COVID-19 and influenza in the population.

Analysing transmission dynamics of HIV/AIDS with optimal control strategy and its controlled state

HIV is a virus that weakens a person's immune system. HIV has three stages, and AIDS is the most severe stage of HIV (Stage 3). People with HIV should take medicine (called ART) recommended by WHO as soon as possible to reduce the amount of virus in the body. In this paper, we formulate a mathematical model for HIV/AIDS with a new approach by focusing on two groups of infectious individuals, HIV and AIDS. We also introduce a controlled class (treated patients and being monitored), and people in this class can spread the disease. We further investigate the essential dynamics of the model through an equilibrium analysis. Optimal control theory is applied to explore effective treatment strategies by combining two control measures: standard antiretroviral therapy and AIDS treatments. Numerical simulation results show the effects of the two time-dependent controls, and they can be used as guidelines for public health interventions.

Optimal policies for mitigating pandemic costs: a minimal model

There have been a number of pharmaceutical and non-pharmaceutical interventions associated with COVID-19 over the past two years. Of the various non-pharmaceutical interventions that were proposed and implemented to control the spread of the COVID-19 pandemic partial and complete lockdowns were used repeatedly in an attempt to minimize the costs associated with mortality, economic losses and social factors, while being subject to constraints such as finite hospital capacity. Here, we use a minimal model to understand the costs and benefits of these strategies that mitigate pandemic costs subject to constraints, we adopt the language of optimal control theory. This allows us to determine top-down policies for the nature and dynamics of social contact rates given an age-structured model for the dynamics of the disease. Depending on the relative weights allocated to mortality and socioeconomic losses, we see that the optimal strategies range from long-term social-distancing only for the most vulnerable, to partial lockdown to ensure not over-running hospitals, to alternating-shifts with significant reduction in mortality and/or socioeconomic losses. Crucially, commonly used strategies that involve long periods of broad lockdown are almost never optimal, as they are highly unstable to reopening {and entail high socioeconomic costs}. Using parameter estimates from data available for Germany and the USA early in the pandemic, we quantify these policies and use sensitivity analysis in the relevant model parameters and initial conditions to determine the range of robustness of our policies. Finally we also discuss how bottom-up behavioral changes affect the dynamics of the pandemic and show they can work in tandem with top-down control policies to mitigate pandemic costs even more effectively.

An integrated simulation framework for the prevention and mitigation of pandemics caused by airborne pathogens

In this work, we developed an integrated simulation framework for pandemic prevention and mitigation of pandemics caused by airborne pathogens, incorporating three sub-models, namely the spatial model, the mobility model, and the propagation model, to create a realistic simulation environment for the evaluation of the effectiveness of different countermeasures on the epidemic dynamics. The spatial model converts images of real cities obtained from Google Maps into undirected weighted graphs that capture the spatial arrangement of the streets utilized next for the mobility of individuals. The mobility model implements a stochastic agent-based approach, developed to assign specific routes to individuals moving in the city, through the use of stochastic processes, utilizing the weights of the underlying graph to deploy shortest path algorithms. The propagation model implements both the epidemiological model and the physical substance of the transmission of an airborne pathogen (in our approach, we investigate the transmission parameters of SARS-CoV-2). The deployment of a set of countermeasures was investigated in reducing the spread of the pathogen, where, through a series of repetitive simulation experiments, we evaluated the effectiveness of each countermeasure in pandemic prevention.

Mathematical models for assessing vaccination scenarios in several provinces in Indonesia

To mitigate casualties from the COVID-19 outbreak, this study aims at assessing the optimal vaccination scenarios, considering several existing healthcare conditions and assumptions, by developing SIQRD (Susceptible-Infected-Quarantine-Recovery-Death) models for Jakarta, West Java, and Banten, in Indonesia. The models include an age-structured dynamic transmission model that naturally allows for different treatments among different age groups of the population. The simulation results show that the timing and period of the vaccination should be well planned and prioritizing particular age groups will give a significant impact on the total number of casualties.

Assessing different interventions against Avian Influenza A (H7N9) infection by an epidemiological model

This paper aims at evaluating the effectiveness of different intervention measures against the infection of avian influenza A (H7N9) by using an epidemiological model. The model formulates the intrinsic interactions of domestic poultry (DP), H7N9 virus and humans by ordinary differential equations and couples the essential roles of various interventions (including culling, vaccinating, screening, disinfecting, and reducing contact rate, etc). Qualitative analysis indicates that when the recruiting poultry is virus-free, there is a transmission threshold denoted by basic reproduction number which can determine the invasion of H7N9; and there is always a stable H7N9 endemic in case of persistent import of virus-carrying poultry, under which only complete vaccination or cutting off poultry-to-poultry/human contacts can stop H7N9 transmission. By performing numerical analysis of the model with biological background parameters, the intervention outcomes against H7N9 infection are further quantified. It is found that (1) reducing poultry-human/poultry interaction and per-contact infection probability, as well as culling DP, are highly effective in diminishing the infections of humans and DP; (2) the disease is prevented when larger than (1 − 0.1λ_p) proportion of DP is vaccinated, where λ_p is the DP-to-DP transmission rate; (3) cleaning and disinfecting environment play limited role in reducing the risk of infection; and (4) screening imported poultry is quite important for stopping disease diffusion, but it works little when local epidemic is prevailing. Combing these measures with real situations would be necessary for controlling H7N9 epidemics and reaching one health purpose.

Optimal COVID-19 Vaccine Sharing Between Two Nations That Also Have Extensive Travel Exchanges

Countries around the world have observed reduced infections from the SARS-CoV-2 virus, that causes COVID-19 illness, primarily due to non-pharmaceutical interventions (NPIs) such as lockdowns and social distancing measures designed to limit physical proximity between people. However, economies and societal interactions require restarting, and so lockdowns cannot continue indefinitely. Therefore, much hope is placed in using newly developed vaccines as a route back to normality, but this raises key questions about how they are shared. There are also emerging questions regarding travel. For instance, international business and trade necessitates at least some in-person exchanges, alongside restarting travel also for tourist purposes. By utilising a Susceptible-Infected-Recovered-Vaccinated (SIRV) mathematical model, we simulate the populations of two nations in parallel, where the first nation produces a vaccine and decides the extent to which it is shared with the second. Overlaying our mathematical structure is the virus-related effects of travel between the two nations. We find that even with extensive travel, nation one minimises its total number of deaths by simply retaining vaccines, aiming for full inoculation as fast as possible, suggesting that the risks posed by travel can be mitigated by rapidly vaccinating its own population. If instead we consider the total deaths i.e., sum of deaths of both nations, then such a policy of not sharing by nation one until full vaccination is highly sub-optimal. A policy of low initial sharing causes many more deaths in nation two than lives saved in nation one, raising important ethical issues. This imbalance in the health impact of vaccination provision must be considered as some countries begin to approach the point of extensive vaccination, while others lack the resources to do so.

State estimation-based control of COVID-19 epidemic before and after vaccine development

In this study, a nonlinear robust control policy is designed together with a state observer in order to manage the novel coronavirus disease (COVID-19) outbreak having an uncertain epidemiological model with unmeasurable variables. This nonlinear model for the COVID-19 epidemic includes eight state variables (susceptible, exposed, infected, quarantined, hospitalized, recovered, deceased, and insusceptible populations). Two plausible scenarios are put forward in this article to control this epidemic before and after its vaccine invention. In the first scenario, the social distancing and hospitalization rates are employed as two applicable control inputs to diminish the exposed and infected groups. However, in the second scenario after the vaccine development, the vaccination rate is taken into account as the third control input to reduce the susceptible populations, in addition to the two objectives of the first scenario. The proposed feedback control measures are defined in terms of the hospitalized and deceased populations due to the available statistical data, while other unmeasurable compartmental variables are estimated by an extended Kalman filter (EKF). In other words, the susceptible, exposed, infected, quarantined, recovered, and insusceptible individuals cannot be identified precisely because of the asymptomatic infection of COVID-19 in some cases, its incubation period, and the lack of an adequate community screening. Utilizing the Lyapunov theorem, the stability and bounded tracking convergence of the closed-loop epidemiological system are investigated in the presence of modeling uncertainties. Finally, a comprehensive simulation study is conducted based on Canada's reported cases for two defined timing plans (with different treatment rates). Obtained results demonstrate that the developed EKF-based control scheme can achieve desired epidemic goals (exponential decrease of infected, exposed, and susceptible people).

MODELING CHOLERA TRANSMISSION UNDER DISEASE CONTROL MEASURES

We present a new mathematical model to investigate the transmission dynamics of cholera under disease control measures that include education programs and water sanitation. The model incorporates the impact of education programs into the disease transmission rates and that of water sanitation into the environmental pathogen dynamics. We conduct a detailed analysis to the autonomous system of the model and establish the local and global stabilities of its equilibria that characterize the threshold dynamics of cholera. We then perform an optimal control study on the general model with time-dependent controls and explore effective approaches to implement the education programs and water sanitation while balancing their costs. Our analysis and simulation highlight the complex interaction among the direct and indirect transmission pathways of the disease, the intrinsic growth of the environmental pathogen and the impact of multiple control measures, and their roles in collectively shaping the transmission dynamics of cholera.

Effective control measures considering spatial heterogeneity to mitigate the 2016-2017 avian influenza epidemic in the Republic of Korea

During the winter of 2016-2017, an epidemic of highly pathogenic avian influenza (HPAI) led to high mortality in poultry and put a serious burden on the poultry industry of the Republic of Korea. Effective control measures considering spatial heterogeneity to mitigate the HPAI epidemic is still a challenging issue. Here we develop a spatial-temporal compartmental model that incorporates the culling rate as a function of the reported farms and farm density in each town. The epidemiological and geographical data of two species, chickens and ducks, from the farms in the sixteen towns in Eumseong-gun and Jincheon-gun are used to find the best-fitted parameters of the metapopulation model. The best culling radius to maximize the final size of the susceptible farms and minimize the total number of culled farms is calculated from the model. The local reproductive number using the next generation method is calculated as an indicator of virus transmission in a given area. Simulation results indicate that this parameter is strongly influenced not only by epidemiological factors such as transmissibility and/or susceptibility of poultry species but also by geographical and demographical factors such as the distribution of poultry farms (or density) and connectivity (or distance) between farms. Based on this result, we suggest the best culling radius with respect to the local reproductive number in a targeted area.

Optimal time-profiles of public health intervention to shape voluntary vaccination for childhood diseases

In order to seek the optimal time-profiles of public health systems (PHS) Intervention to favor vaccine propensity, we apply optimal control (OC) to a SIR model with voluntary vaccination and PHS intervention. We focus on short-term horizons, and on both continuous control strategies resulting from the forward-backward sweep deterministic algorithm, and piecewise-constant strategies (which are closer to the PHS way of working) investigated by the simulated annealing (SA) stochastic algorithm. For childhood diseases, where disease costs are much larger than vaccination costs, the OC solution sets at its maximum for most of the policy horizon, meaning that the PHS cannot further improve perceptions about the net benefit of immunization. Thus, the subsequent dynamics of vaccine uptake stems entirely from the declining perceived risk of infection (due to declining prevalence) which is communicated by direct contacts among parents, and unavoidably yields a future decline in vaccine uptake. We find that for relatively low communication costs, the piecewise control is close to the continuous control. For large communication costs the SA algorithm converges towards a non-monotone OC that can have oscillations.

Optimal treatment strategy of an avian influenza model with latency

Avian influenza, caused by influenza A viruses, has received worldwide attention over recent years. In this study, we formulate a mathematical model for avian influenza that includes human–human transmission and incorporates the effects of infection latency and treatments. We investigate the essential dynamics of the model through an equilibrium analysis. Meanwhile, we explore effective treatment strategies to control avian influenza outbreaks using optimal control theory. Our results show that strategically deployed medical treatments can significantly reduce the numbers of exposed and infection persons.

Perspectives on optimal control of varicella and herpes zoster by mass routine varicella vaccination

Herpes zoster arises from reactivation of the varicella-zoster virus (VZV), causing varicella in children. As reactivation occurs when cell-mediated immunity (CMI) declines, and there is evidence that re-exposure to VZV boosts CMI, mass varicella immunization might increase the zoster burden, at least for some decades. Fear of this natural zoster boom is the main reason for the paralysis of varicella immunization in Europe. We apply optimal control to a realistically parametrized age-structured model for VZV transmission and reactivation to investigate whether feasible varicella immunization paths that are optimal in controlling both varicella and zoster exist. We analyse the optimality system numerically focusing on the role of the cost functional, of the relative zoster-varicella cost and of the planning horizon length. We show that optimal programmes will mostly be unfeasible for public health owing to their complex temporal profiles. This complexity is the consequence of the intrinsically antagonistic nature of varicella immunization programmes when aiming to control both varicella and zoster. However, we show that gradually increasing-hence feasible-vaccination schedules can perform better than routine programmes with constant vaccine uptake. Finally, we show the optimal profiles of feasible programmes targeting mitigation of the post-immunization natural zoster boom with priority.

Modeling the role of information and limited optimal treatment on disease prevalence

Disease outbreaks induce behavioural changes in healthy individuals to avoid contracting infection. We first propose a compartmental model which accounts for the effect of individual's behavioural response due to information of the disease prevalence. It is assumed that the information is growing as a function of infective population density that saturates at higher density of infective population and depends on active educational and social programmes. Model analysis has been performed and the global stability of equilibrium points is established. Further, choosing the treatment (a pharmaceutical intervention) and the effect of information (a non-pharmaceutical intervention) as controls, an optimal control problem is formulated to minimize the cost and disease fatality. In the cost functional, the nonlinear effect of controls is accounted. Analytical characterization of optimal control paths is done with the help of Pontryagin's Maximum Principle. Numerical findings suggest that if only control via information is used, it is effective and economical for early phase of disease spread whereas treatment works well for long term control except for initial phase. Furthermore, we observe that the effect of information induced behavioural response plays a crucial role in the absence of pharmaceutical control. Moreover, comprehensive use of both the control interventions is more effective than any single applied control policy and it reduces the number of infective individuals and minimizes the economic cost generated from disease burden and applied controls. Thus, the combined effect of both the control policies is found more economical during the entire epidemic period whereas the implementation of a single policy is not found economically viable.

Nonlinear dynamics of avian influenza epidemic models

Avian influenza is a zoonotic disease caused by the transmission of the avian influenza A virus, such as H5N1 and H7N9, from birds to humans. The avian influenza A H5N1 virus has caused more than 500 human infections worldwide with nearly a 60% death rate since it was first reported in Hong Kong in 1997. The four outbreaks of the avian influenza A H7N9 in China from March 2013 to June 2016 have resulted in 580 human cases including 202 deaths with a death rate of nearly 35%. In this paper, we construct two avian influenza bird-to-human transmission models with different growth laws of the avian population, one with logistic growth and the other with Allee effect, and analyze their dynamical behavior. We obtain a threshold value for the prevalence of avian influenza and investigate the local or global asymptotical stability of each equilibrium of these systems by using linear analysis technique or combining Liapunov function method and LaSalle's invariance principle, respectively. Moreover, we give necessary and sufficient conditions for the occurrence of periodic solutions in the avian influenza system with Allee effect of the avian population. Numerical simulations are also presented to illustrate the theoretical results.

On avian influenza epidemic models with time delay

After the outbreak of the first avian influenza A virus (H5N1) in Hong Kong in 1997, another avian influenza A virus (H7N9) crossed the species barrier in mainland China in 2013 and 2014 and caused more than 400 human cases with a death rate of nearly 40%. In this paper, we take account of the incubation periods of avian influenza A virus and construct a bird-to-human transmission model with different time delays in the avian and human populations combining the survival probability of the infective avian and human populations at the latent time. By analyzing the dynamical behavior of the model, we obtain a threshold value for the prevalence of avian influenza and investigate local and global asymptotical stability of equilibria of the system.

Mathematical Analysis of the Effects of HIV-Malaria Co-infection on Workplace Productivity

In this paper, a nonlinear dynamical system is proposed and qualitatively analyzed to study the dynamics and effects of HIV-malaria co-infection in the workplace. Basic reproduction numbers of sub-models are derived and are shown to have LAS disease-free equilibria when their respective basic reproduction numbers are less than unity. Conditions for existence of endemic equilibria of sub-models are also derived. Unlike the HIV-only model, the malaria-only model is shown to exhibit a backward bifurcation under certain conditions. Conditions for optimal control of the co-infection are derived using the Pontryagin's maximum principle. Numerical experimentation on the resulting optimality system is performed. Using the incremental cost-effectiveness ratio, it is observed that combining preventative measures for both diseases is the best strategy for optimal control of HIV-malaria co-infection at the workplace.

Global dynamics of avian influenza epidemic models with psychological effect

Cross-sectional surveys conducted in Thailand and China after the outbreaks of the avian influenza A H5N1 and H7N9 viruses show a high degree of awareness of human avian influenza in both urban and rural populations, a higher level of proper hygienic practice among urban residents, and in particular a dramatically reduced number of visits to live markets in urban population after the influenza A H7N9 outbreak in China in 2013. In this paper, taking into account the psychological effect toward avian influenza in the human population, a bird-to-human transmission model in which the avian population exhibits saturation effect is constructed. The dynamical behavior of the model is studied by using the basic reproduction number. The results demonstrate that the saturation effect within avian population and the psychological effect in human population cannot change the stability of equilibria but can affect the number of infected humans if the disease is prevalent. Numerical simulations are given to support the theoretical results and sensitivity analyses of the basic reproduction number in terms of model parameters that are performed to seek for effective control measures for avian influenza.

Optimal control of epidemic information dissemination over networks

Information dissemination control is of crucial importance to facilitate reliable and efficient data delivery, especially in networks consisting of time-varying links or heterogeneous links. Since the abstraction of information dissemination much resembles the spread of epidemics, epidemic models are utilized to characterize the collective dynamics of information dissemination over networks. From a systematic point of view, we aim to explore the optimal control policy for information dissemination given that the control capability is a function of its distribution time, which is a more realistic model in many applications. The main contributions of this paper are to provide an analytically tractable model for information dissemination over networks, to solve the optimal control signal distribution time for minimizing the accumulated network cost via dynamic programming, and to establish a parametric plug-in model for information dissemination control. In particular, we evaluate its performance in mobile and generalized social networks as typical examples.

Decision Support System for Sanitary Teams Activities

This paper describes the information system that has been built for the support of sanitary teams. The system is aimed at supporting analytical work which must be carried out when there is a risk of an epidemic outbreak. It is meant to provide tools for predicting the size of an epidemic on the basis of the actual data collected during its course. Since sanitary teams try to control the size of the epidemics such a tool must model also sanitary teams activities. As a result a model for the prediction can be quite complicated in terms of the number of equations it contains. Furthermore, since a model is based on several parameters there must be a tool for finding these parameters on the basis on the actual data corresponding to the epidemic evolution. The paper describes the proposition of such a system. It presents, in some details, the main components of the system. In particular, the environment for building complex models (containing not only the epidemic model but also activities of sanitary teams trying to inhibit the epidemic) is discussed. Then, the module for a model calibration is presented. The module is a part of server for solving optimal control problems and can be accessed via Internet. Finally, this paper shows how optimal control problems can be constructed with the aim of the efficient epidemic management. Some optimal control problems related to that issue are discussed and numerical results of its solution are presented.

Optimal control of HIV/AIDS in the workplace in the presence of careless individuals

A nonlinear dynamical system is proposed and qualitatively analyzed to study the dynamics of HIV/AIDS in the workplace. The disease-free equilibrium point of the model is shown to be locally asymptotically stable if the basic reproductive number, ℛ0, is less than unity and the model is shown to exhibit a unique endemic equilibrium when the basic reproductive number is greater than unity. It is shown that, in the absence of recruitment of infectives, the disease is eradicated when ℛ0 < 1, whiles the disease is shown to persist in the presence of recruitment of infected persons. The basic model is extended to include control efforts aimed at reducing infection, irresponsibility, and nonproductivity at the workplace. This leads to an optimal control problem which is qualitatively analyzed using Pontryagin's Maximum Principle (PMP). Numerical simulation of the resulting optimal control problem is carried out to gain quantitative insights into the implications of the model. The simulation reveals that a multifaceted approach to the fight against the disease is more effective than single control strategies.

Optimal tuberculosis prevention and control strategy from a mathematical model based on real data

A mathematical control model for the transmission dynamics of tuberculosis (TB) in South Korea is developed on the basis of the reported active-TB and relapse-TB incidence data. In this work, optimal control theory is used to propose optimal TB prevention and control strategy and rearrange the government TB budget for the best TB elimination plan. The impact of distancing, case finding, and/or case holding controls are investigated when the number of infected and infectious individuals are minimized, while the intervention costs are kept low. The implementation of optimal control measures shows that the distancing control, such as isolation of infectious people, early TB patient detection, and educational program/campaign for healthy control, is the most effective control factor for the prevention of TB transmission in South Korea.

Optimal control of a two-strain tuberculosis-HIV/AIDS co-infection model

Tuberculosis is a bacterial disease caused by Mycobacterium tuberculosis (TB). The risk for TB infection greatly increases with HIV infection; TB disease occurs in 7-10% of patients with HIV infection each year, increasing the potential for transmission of drug-resistant Mycobacterium tuberculosis strains. In this paper a deterministic model is presented and studied for the transmission of TB-HIV/AIDS co-infection. Optimal control theory is then applied to investigate optimal strategies for controlling the spread of the disease using treatment of infected individuals with TB as the system control variables. Various combination strategies were examined so as to investigate the impact of the controls on the spread of the disease. And incremental cost-effectiveness ratio (ICER) was used to investigate the cost effectiveness of all the control strategies. Our results show that the implementation of the combination strategy involving the prevention of treatment failure in drug-sensitive TB infectious individuals and the treatment of individuals with drug-resistant TB is the most cost-effective control strategy. Similar results were obtained with different objective functionals involving the minimization of the number of individuals with drug-sensitive TB-only and drug-resistant TB-only with the efforts involved in applying the control.

Simulating optimal vaccination times during cholera outbreaks

The use of cholera vaccines has been increasingly recognized as an effective control measure in cholera endemic countries. However, guidelines for using vaccination during cholera outbreaks are still to be established, and it remains an open question as to how and when the vaccines should be deployed to best control ongoing cholera outbreaks. Here we formulate a new optimal control model to assess the value of cholera vaccines in epidemic settings and cost-effective optimal times to deploy a vaccine. Our results suggest that as long as the vaccine prices are sufficiently low, vaccination should always start from or immediately after the onset of a cholera outbreak.

Optimized strategy for the control and prevention of newly emerging influenza revealed by the spread dynamics model

No matching vaccine is immediately available when a novel influenza strain breaks out. Several nonvaccine-related strategies must be employed to control an influenza epidemic, including antiviral treatment, patient isolation, and immigration detection. This paper presents the development and application of two regional dynamic models of influenza with Pontryagin's Maximum Principle to determine the optimal control strategies for an epidemic and the corresponding minimum antiviral stockpiles. Antiviral treatment was found to be the most effective measure to control new influenza outbreaks. In the case of inadequate antiviral resources, the preferred approach was the centralized use of antiviral resources in the early stage of the epidemic. Immigration detection was the least cost-effective; however, when used in combination with the other measures, it may play a larger role. The reasonable mix of the three control measures could reduce the number of clinical cases substantially, to achieve the optimal control of new influenza.

Optimal isolation control strategies and cost-effectiveness analysis of a two-strain avian influenza model

The most important and effective measures against disease outbreaks in the absence of valid medicines or vaccine are quarantine and isolation strategies. In this paper optimal control theory is applied to a system of ordinary differential equation describing a two-strain avian influenza transmission via the Pontryagin's Maximum Principle. To this end, a pair of control variables representing the isolation strategies for individuals with avian and mutant strains were incorporated into the transmission model. The infection averted ratio (IAR) and the incremental cost-effectiveness ratio (ICER) were calculated to investigate the cost-effectiveness of all possible combinations of the control strategies. The simulation results show that the implementation of the combination strategy during the epidemic is the most cost-effective strategy for avian influenza transmission. This is followed by the control strategy involving isolation of individuals with the mutant strain. Also observed was the fact that low mutating and more virulent virus results in an increased control effort of isolating individuals with the avian strain; and high mutating with more virulent virus results in increased efforts in isolating individuals with the mutant strain.

Trends in parameterization, economics and host behaviour in influenza pandemic modelling: a review and reporting protocol

BACKGROUND

The volume of influenza pandemic modelling studies has increased dramatically in the last decade. Many models incorporate now sophisticated parameterization and validation techniques, economic analyses and the behaviour of individuals.

METHODS

We reviewed trends in these aspects in models for influenza pandemic preparedness that aimed to generate policy insights for epidemic management and were published from 2000 to September 2011, i.e. before and after the 2009 pandemic.

RESULTS

We find that many influenza pandemics models rely on parameters from previous modelling studies, models are rarely validated using observed data and are seldom applied to low-income countries. Mechanisms for international data sharing would be necessary to facilitate a wider adoption of model validation. The variety of modelling decisions makes it difficult to compare and evaluate models systematically.

CONCLUSIONS

We propose a model Characteristics, Construction, Parameterization and Validation aspects protocol (CCPV protocol) to contribute to the systematisation of the reporting of models with an emphasis on the incorporation of economic aspects and host behaviour. Model reporting, as already exists in many other fields of modelling, would increase confidence in model results, and transparency in their assessment and comparison.

Optimality of a time-dependent treatment profile during an epidemic

The emergence and spread of drug resistance is one of the most challenging public health issues in the treatment of some infectious diseases. The objective of this work is to investigate whether the effect of resistance can be contained through a time-dependent treatment strategy during the epidemic subject to an isoperimetric constraint. We apply control theory to a population dynamical model of influenza infection with drug-sensitive and drug-resistant strains, and solve the associated control problem to find the optimal treatment profile that minimizes the cumulative number of infections (i.e. the epidemic final size). We consider the problem under the assumption of limited drug stockpile and show that as the size of stockpile increases, a longer delay in start of treatment is required to minimize the total number of infections. Our findings show that the amount of drugs used to minimize the total number of infections depends on the rate of de novo resistance regardless of the initial size of drug stockpile. We demonstrate that both the rate of resistance emergence and the relative transmissibility of the resistant strain play important roles in determining the optimal timing and level of treatment profile.

Impact of vaccine arrival on the optimal control of a newly emerging infectious disease: A theoretical study

When a newly emerging human infectious disease spreads through a host population, it may be that public health authorities must begin facing the outbreaks and planning an intervention campaign when not all intervention tools are readily available. In such cases, the problem of finding optimal intervention strategies to minimize both the disease burden and the intervention costs may be addressed by considering multiple intervention regimes. In this paper, we consider the scenario in which authorities may rely initially only on non-pharmaceutical interventions at the beginning of the campaign, knowing that a vaccine will later be available, at an exogenous and known switching time. We use a two-stage optimal control problem over a finite time horizon to analyze the optimal intervention strategies during the whole campaign, and to assess the effects of the new intervention tool on the preceding stage of the campaign. We obtain the optimality systems of two connected optimal control problems, and show the solution profiles through numerical simulations.

ON THE OPTIMAL VACCINATION STRATEGIES FOR HORIZONTALLY AND VERTICALLY TRANSMITTED INFECTIOUS DISEASES

We consider an SEIR epidemic model for an infectious disease that spreads in the human host population through both horizontal and vertical transmission. A periodically varying contact rate is introduced to simulate recurrent outbreaks. We use the optimal control theory to assess the disease control. Optimal vaccination strategies to minimize both the disease burden and the intervention costs are analyzed. We derive the optimality system and solve it numerically. The theoretical findings are then used to simulate a vaccination campaign for rubella under several scenarios, by using epidemiological parameters obtained by real data.

A simple analysis of vaccination strategies for rubella

We consider an SEIR epidemic model with vertical transmission introduced by Li, Smith and Wang, [23], and apply optimal control theory to assess the effects of vaccination strategies on the model dynamics. The strategy is chosen to minimize the total number of infectious individuals and the cost associated with vaccination. We derive the optimality system and solve it numerically. The theoretical findings are then used to simulate a vaccination campaign for rubella in China.

An evolutionary model of influenza A with drift and shift

Influenza A virus evolves through two types of evolutionary mechanisms - drift and shift. These two evolutionary mechanisms allow the pathogen to infect us repeatedly, as well as occasionally create pandemics with large morbidity and mortality. Here we introduce a novel model that incorporates both evolutionary mechanisms. This necessitates the modelling of three types of strains - seasonal human strains, bird-to-human transmittable H5N1 strains and evolved pandemic H5N1 strain. We define reproduction and invasion reproduction numbers and use them to establish the presence of dominant and coexistence equilibria. We find that the amino acid substitution structure of human influenza can destabilize the human influenza equilibrium and sustained oscillations are possible. We find that for low levels of infection in domestic birds, these oscillations persist, inducing oscillations in the number of humans infected with the avian flu strain. The oscillations have a period of 365 days, similar to the one that can be observed in the cumulative number of human H5N1 cases reported by the World Health Organization (WHO). Furthermore, we establish some partial global results on the competition of the strains.