scholarly journals Analytical approximation for invasion and endemic thresholds, and the optimal control of epidemics in spatially explicit individual-based models

2021 ◽  
Vol 18 (176) ◽  
Author(s):  
Yevhen F. Suprunenko ◽  
Stephen J. Cornell ◽  
Christopher A. Gilligan
Keyword(s):  
Optimal Control ◽  
Computer Simulations ◽  
Economic Cost ◽  
Analytical Approximation ◽  
Host Population ◽  
Dispersal Kernel ◽  
Control Measures ◽  
Spatially Explicit ◽  
Individual Based Models ◽  
Control Of Epidemics

Computer simulations of individual-based models are frequently used to compare strategies for the control of epidemics spreading through spatially distributed populations. However, computer simulations can be slow to implement for newly emerging epidemics, delaying rapid exploration of different intervention scenarios, and do not immediately give general insights, for example, to identify the control strategy with a minimal socio-economic cost. Here, we resolve this problem by applying an analytical approximation to a general epidemiological, stochastic, spatially explicit SIR(S) model where the infection is dispersed according to a finite-ranged dispersal kernel. We derive analytical conditions for a pathogen to invade a spatially explicit host population and to become endemic. To derive general insights about the likely impact of optimal control strategies on invasion and persistence: first, we distinguish between ‘spatial' and ‘non-spatial' control measures, based on their impact on the dispersal kernel; second, we quantify the relative impact of control interventions on the epidemic; third, we consider the relative socio-economic cost of control interventions. Overall, our study shows a trade-off between the two types of control interventions and a vaccination strategy. We identify the optimal strategy to control invading and endemic diseases with minimal socio-economic cost across all possible parameter combinations. We also demonstrate the necessary characteristics of exit strategies from control interventions. The modelling framework presented here can be applied to a wide class of diseases in populations of humans, animals and plants.

scholarly journals Optimal Control Measures to Combat COVID 19 Spread in Sri Lanka: A Mathematical Model Considering the Heterogeneity of Cases

2020 ◽  
Author(s):  
Tharindu Wickramaarachchi ◽  
Sanjeewa Perera
Keyword(s):  
Public Health ◽  
Mathematical Model ◽  
Optimal Control ◽  
Sri Lanka ◽  
Health System ◽  
Economic Cost ◽  
Control Measures ◽  
Disease Spread ◽  
Local Case ◽  
The Government

The COVID 19 pandemic caused by the novel corona virus (SARS-CoV-2) has been one of the major public health concerns across the globe, currently more than 3.5 million individuals have been infected, and the number of deaths has passed 250,000. The world wide burden of the disease has been massive, and the governments are in dilemma to protect the health system of the country while safeguarding the economy. There is no vaccine or antivirus drug found against this virus while multiple research groups are actively working on a suitable candidate. The only available mode of minimizing the disease burden has been to control its transmission among the population. Since the occurrence of first COVID 19 local case on 11 March 2020, the government of Sri Lanka introduced serious social distancing and public health interventions in its fullest capacity as a developing nation to effectively combat with the disease spread. This study focuses to develop a mathematical model to investigate the dynamic of this novel disease using an extended version of an SEIR compartmental structure considering the heterogeneity of cases such as asymptomatic, symptomatic with mild indications and the cases required intensive care treatments. All the measures and interventions are in progress with a significantly large social and economic cost, thus, optimal control techniques are used to identify the most appropriate strategies to minimize this cost. The results of the simulations prove that optimal control measures can be worked out as the epidemic curves are flattened while delaying the outbreak so that the health system might not be under pressure to treat and care the patients.

scholarly journals Effects of heterogeneity in infection-exposure history and immunity on the dynamics of a protozoan parasite

2007 ◽  
Vol 4 (16) ◽  
pp. 841-849 ◽  
Author(s):  
Maite Severins ◽  
Don Klinkenberg ◽  
Hans Heesterbeek
Keyword(s):  
Dynamic Behaviour ◽  
Protozoan Parasite ◽  
Host Population ◽  
Infection Process ◽  
Control Measures ◽  
Complex Dynamic ◽  
Systems Models ◽  
Exposure History ◽  
The Relationship ◽  
Initial Contamination

Infection systems where traits of the host, such as acquired immunity, interact with the infection process can show complex dynamic behaviour with counter-intuitive results. In this study, we consider the traits ‘immune status’ and ‘exposure history’, and our aim is to assess the influence of acquired individual heterogeneity in these traits. We have built an individual-based model of Eimeria acervulina infections, a protozoan parasite with an environmental stage that causes coccidiosis in chickens. With the model, we simulate outbreaks of the disease under varying initial contaminations. Heterogeneity in the traits arises stochastically through differences in the dose and frequency of parasites that individuals pick up from the environment. We find that the relationship between the initial contamination and the severity of an outbreak has a non-monotonous ‘wave-like’ pattern. This pattern can be explained by an increased heterogeneity in the host population caused by the infection process at the most severe outbreaks. We conclude that when dealing with these types of infection systems, models that are used to develop or evaluate control measures cannot neglect acquired heterogeneity in the host population traits that interact with the infection process.

scholarly journals Parameter-dependent transmission dynamics and optimal control of foot and mouth disease in a contaminated environment

2019 ◽  
Vol 27 (1) ◽  
Author(s):  
Francis Mugabi ◽  
Joseph Mugisha ◽  
Betty Nannyonga ◽  
Henry Kasumba ◽  
Margaret Tusiime
Keyword(s):  
Optimal Control ◽  
Deterministic Model ◽  
Foot And Mouth Disease ◽  
Decay Rates ◽  
Mouth Disease ◽  
Control Measures ◽  
Transmission Dynamics ◽  
Optimality System ◽  
Foot And Mouth ◽  
Environmental Decontamination

AbstractThe problem of foot and mouth disease (FMD) is of serious concern to the livestock sector in most nations, especially in developing countries. This paper presents the formulation and analysis of a deterministic model for the transmission dynamics of FMD through a contaminated environment. It is shown that the key parameters that drive the transmission of FMD in a contaminated environment are the shedding, transmission, and decay rates of the virus. Using numerical results, it is depicted that the host-to-host route is more severe than the environmental-to-host route. The model is then transformed into an optimal control problem. Using the Pontryagin’s Maximum Principle, the optimality system is determined. Utilizing a gradient type algorithm with projection, the optimality system is solved for three control strategies: optimal use of vaccination, environmental decontamination, and a combination of vaccination and environmental decontamination. Results show that a combination of vaccination and environmental decontamination is the most optimal strategy. These results indicate that if vaccination and environmental decontamination are used optimally during an outbreak, then FMD transmission can be controlled. Future studies focusing on the control measures for the transmission of FMD in a contaminated environment should aim at reducing the transmission and the shedding rates, while increasing the decay rate.

scholarly journals Estimating Economic Losses Caused by COVID-19 under Multiple Control Measure Scenarios with a Coupled Infectious Disease—Economic Model: A Case Study in Wuhan, China

2021 ◽  
Vol 18 (22) ◽  
pp. 11753
Author(s):  
Xingtian Chen ◽  
Wei Gong ◽  
Xiaoxu Wu ◽  
Wenwu Zhao
Keyword(s):  
Infectious Disease ◽  
Economic Model ◽  
Control Measure ◽  
Central Valley ◽  
Economic Cost ◽  
Assessment Method ◽  
Control Measures ◽  
Economic Losses ◽  
Multiple Control ◽  
Health Crisis

Background: The outbreak of the COVID-19 epidemic has caused an unprecedented public health crisis and drastically impacted the economy. The relationship between different control measures and economic losses becomes a research hotspot. Methods: In this study, the SEIR infectious disease model was revised and coupled with an economic model to quantify this nonlinear relationship in Wuhan. The control measures were parameterized into two factors: the effective number of daily contacts (people) (r); the average waiting time for quarantined patients (day) (g). Results: The parameter r has a threshold value that if r is less than 5 (people), the number of COVID-19 infected patients is very close to 0. A “central valley” around r = 5~6 can be observed, indicating an optimal control measure to reduce economic losses. A lower value of parameter g is beneficial to stop COVID-19 spread with a lower economic cost. Conclusion: The simulation results demonstrate that implementing strict control measures as early as possible can stop the spread of COVID-19 with a minimal economic impact. The quantitative assessment method in this study can be applied in other COVID-19 pandemic areas or countries.

scholarly journals Fractional-Order Modelling and Optimal Control of Cholera Transmission

2021 ◽  
Vol 5 (4) ◽  
pp. 261
Author(s):  
Silvério Rosa ◽  
Delfim F. M. Torres
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Sensitivity Analysis ◽  
Fractional Order ◽  
Control Measures ◽  
Time Interval ◽  
Variable Order ◽  
Effectiveness Analysis ◽  
The Cost ◽  
Derivative Order

A Caputo-type fractional-order mathematical model for “metapopulation cholera transmission” was recently proposed in [Chaos Solitons Fractals 117 (2018), 37–49]. A sensitivity analysis of that model is done here to show the accuracy relevance of parameter estimation. Then, a fractional optimal control (FOC) problem is formulated and numerically solved. A cost-effectiveness analysis is performed to assess the relevance of studied control measures. Moreover, such analysis allows us to assess the cost and effectiveness of the control measures during intervention. We conclude that the FOC system is more effective only in part of the time interval. For this reason, we propose a system where the derivative order varies along the time interval, being fractional or classical when more advantageous. Such variable-order fractional model, that we call a FractInt system, shows to be the most effective in the control of the disease.

scholarly journals Socially vs. Privately Optimal Control of Livestock Diseases: A Case for Integration of Epidemiology and Economics

2020 ◽  
Vol 7 ◽  
Author(s):  
Ângelo J. Mendes ◽  
Daniel T. Haydon ◽  
Emma McIntosh ◽  
Nick Hanley ◽  
Jo E. B. Halliday
Keyword(s):  
Optimal Control ◽  
Disease Control ◽  
Low Income ◽  
Disease Risk ◽  
Control Measures ◽  
Low Income Countries ◽  
Control Effort ◽  
Optimal Behavior ◽  
Wide Range ◽  
Livestock Diseases

This paper aims to illustrate the interdependencies between key epidemiological and economic factors that influence the control of many livestock infectious diseases. The factors considered here are (i) farmer heterogeneity (i.e., differences in how farmers respond to a perceived disease risk), (ii) off-farm effects of farmers' actions to control a disease (i.e., costs and benefits borne by agents that are external to the farm), and (iii) misalignment between privately and socially optimal control efforts (i.e., privately optimal behavior not conducive to a socially optimal outcome). Endemic chronic diseases cause a wide range of adverse social and economic impacts, particularly in low-income countries. The actions taken by farmers to control livestock diseases minimize some of these impacts, and heterogeneity in those actions leads to variation in prevalence at the farm level. While some farmers respond to perceived disease risks, others free-ride on the actions of these individuals, thereby compromising the potential benefits of collective, coordinated behavior. When evaluating a plausible range of disease cost to price of control ratios and assuming that farmers choose their privately optimal control effort, we demonstrate that achievement of a socially optimal disease control target is unlikely, occurring in <25% of all price-cost combinations. To achieve a socially optimal disease control outcome (reliant on farmers' voluntary actions), control policies must consider farmer heterogeneity, off-farm effects, and the predicted uptake of control measures under the assumption of optimized behavior.

scholarly journals Optimal control of epidemics in metapopulations

2009 ◽  
Vol 6 (41) ◽  
pp. 1135-1144 ◽  
Author(s):  
Robert E. Rowthorn ◽  
Ramanan Laxminarayan ◽  
Christopher A. Gilligan
Keyword(s):  
Optimal Control ◽  
Disease Control ◽  
The Other ◽  
Control Methods ◽  
Scarce Resources ◽  
Total Level ◽  
Infection Treatment ◽  
Control Of Epidemics ◽  
Optimal Control Methods

Little is known about how best to deploy scarce resources for disease control when epidemics occur in different but interconnected regions. We use a combination of optimal control methods and epidemiological theory for metapopulations to address this problem. We consider what strategy should be used if the objective is to minimize the discounted number of infected individuals during the course of an epidemic. We show, for a system with two interconnected regions and an epidemic in which infected individuals recover and can be reinfected, that equalizing infection in the two regions is the worst possible strategy in minimizing the total level of infection. Treatment should instead be preferentially directed at the region with the lower level of infection, treating the other subpopulation only when there is resource left over. The same strategy holds with preferential treatments of regions with lower levels of infection when quarantine is introduced.

scholarly journals Modeling the Effects of Helminth Infection on the Transmission Dynamics of Mycobacterium tuberculosis under Optimal Control Strategies

2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
Aristide G. Lambura ◽  
Gasper G. Mwanga ◽  
Livingstone Luboobi ◽  
Dmitry Kuznetsov
Keyword(s):  
Optimal Control ◽  
Equilibrium Point ◽  
Drug Administration ◽  
Mass Drug Administration ◽  
Helminth Infection ◽  
Reproduction Number ◽  
Control Strategies ◽  
Active Tuberculosis ◽  
Control Measures ◽  
The Impact

A deterministic mathematical model for the transmission and control of cointeraction of helminths and tuberculosis is presented, to examine the impact of helminth on tuberculosis and the effect of control strategies. The equilibrium point is established, and the effective reproduction number is computed. The disease-free equilibrium point is confirmed to be asymptotically stable whenever the effective reproduction number is less than the unit. The analysis of the effective reproduction number indicates that an increase in the helminth cases increases the tuberculosis cases, suggesting that the control of helminth infection has a positive impact on controlling the dynamics of tuberculosis. The possibility of bifurcation is investigated using the Center Manifold Theorem. Sensitivity analysis is performed to determine the effect of every parameter on the spread of the two diseases. The model is extended to incorporate control measures, and Pontryagin’s Maximum Principle is applied to derive the necessary conditions for optimal control. The optimal control problem is solved numerically by the iterative scheme by considering vaccination of infants for Mtb, treatment of individuals with active tuberculosis, mass drug administration with regular antihelminthic drugs, and sanitation control strategies. The results show that a combination of educational campaign, treatment of individuals with active tuberculosis, mass drug administration, and sanitation is the most effective strategy to control helminth-Mtb coinfection. Thus, to effectively control the helminth-Mtb coinfection, we suggest to public health stakeholders to apply intervention strategies that are aimed at controlling helminth infection and the combination of vaccination of infants and treatment of individuals with active tuberculosis.

scholarly journals Stability Analysis and Optimal Control of a Vector-Borne Disease with Nonlinear Incidence

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Muhammad Ozair ◽  
Abid Ali Lashari ◽  
Il Hyo Jung ◽  
Kazeem Oare Okosun
Keyword(s):  
Optimal Control ◽  
Sensitivity Analysis ◽  
Control Measures ◽  
Basic Reproductive Number ◽  
Control Technique ◽  
Global Dynamics ◽  
Nonlinear Incidence ◽  
Vector Borne Disease ◽  
Vector Borne ◽  
The Impact

The paper considers a model for the transmission dynamics of a vector-borne disease with nonlinear incidence rate. It is proved that the global dynamics of the disease are completely determined by the basic reproduction number. In order to assess the effectiveness of disease control measures, the sensitivity analysis of the basic reproductive numberR0and the endemic proportions with respect to epidemiological and demographic parameters are provided. From the results of the sensitivity analysis, the model is modified to assess the impact of three control measures; the preventive control to minimize vector human contacts, the treatment control to the infected human, and the insecticide control to the vector. Analytically the existence of the optimal control is established by the use of an optimal control technique and numerically it is solved by an iterative method. Numerical simulations and optimal analysis of the model show that restricted and proper use of control measures might considerably decrease the number of infected humans in a viable way.

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