scholarly journals Implicit versus explicit control strategies in models for vector-borne disease epidemiology

2019 ◽  
Author(s):  
Jeffery Demers ◽  
Suzanne L. Robertson ◽  
Sharon Bewick ◽  
William F. Fagan
Keyword(s):  
Optimal Control ◽  
Disease Modeling ◽  
Control Strategies ◽  
Disease Suppression ◽  
Disease Spread ◽  
Model Parameters ◽  
Vector Borne Disease ◽  
Vector Population ◽  
Vector Borne ◽  
Implicit And Explicit

AbstractThroughout the vector-borne disease modeling literature, there exist two general frameworks for incorporating vector management strategies (e.g. area-wide adulticide spraying and larval source reduction campaigns) into vector population models, namely, the “implicit” and “explicit” control frameworks. The more simplistic “implicit” framework facilitates derivation of mathematically rigorous results on disease suppression and optimal control, but the biological connection of these results to realworld “explicit” control actions that could guide specific management actions is vague at best. Here, we formally define the biological and mathematical relationships between implicit and explicit control, and we provide detailed mathematical expressions relating the strength of implicit control to management-relevant properties of explicit control for four common intervention strategies. These expressions allow optimal control and sensitivity analysis results in existing implicit control studies to be interpreted in terms of real world actions. Our work reveals a previously unknown fact: implicit control is a meaningful approximation of explicit control only when resonance-like synergistic effects between multiple controls have a negligible effect on average population reduction. When non-negligible synergy exists, implicit control results, despite their mathematical tidiness, fail to provide accurate predictions regarding vector control and disease spread. The methodology we establish can be applied to study the interaction of phenological effects with control strategies, and we present a new technique for finding impulse control strategies that optimally reduce a vector population in the presence of seasonally oscillating model parameters. Collectively, these elements build an effective bridge between analytically interesting and mathematically tractable implicit control and the challenging, action-oriented explicit control.

Vector Control, Optimal Control, and Vector-Borne Disease Dynamics

2020 ◽  
pp. 267-288
Author(s):  
Michael B. Bonsall
Keyword(s):  
Optimal Control ◽  
Population Genetics ◽  
Population Dynamics ◽  
Vector Control ◽  
Cost Effective ◽  
Disease Suppression ◽  
Medical Interventions ◽  
Vector Borne Disease ◽  
Vector Borne

Understanding methods of vector control is essential to vector-borne disease (VBD) management. Vaccines or standard medical interventions for many VDBs do not exist or are poorly developed so disease control is focused on managing vector numbers and dynamics. This involves understanding not only the population dynamics but also the population genetics of vectors. Using mosquitoes as a case study, in this chapter, the modern genetics-based methods of vector control (self-limiting, self-sustaining) on mosquito population and disease suppression will be reviewed. These genetics-based methods highlight the importance of understanding the interplay between genetics and ecology to develop optimal, cost-effective solutions for control. The chapter focuses on how these genetics-based methods can be integrated with other interventions, and concludes with a summary of regulatory and policy perspectives about the use of these approaches in the management of VBDs.

Mathematical modeling and projections of a vector-borne disease with optimal control strategies: A case study of the Chikungunya in Chad

2021 ◽  
Vol 150 ◽  
pp. 111197
Author(s):  
Hamadjam Abboubakar ◽  
Albert Kouchéré Guidzavaï ◽  
Joseph Yangla ◽  
Irépran Damakoa ◽  
Ruben Mouangue
Keyword(s):  
Mathematical Modeling ◽  
Optimal Control ◽  
Control Strategies ◽  
Vector Borne Disease ◽  
Vector Borne

scholarly journals Basic Properties and Qualitative Dynamics of a Vector-Borne Disease Model with Vector Stages and Vertical Transmission

2018 ◽  
Vol 2018 ◽  
pp. 1-16
Author(s):  
Sansao A. Pedro
Keyword(s):  
Vertical Transmission ◽  
Control Strategies ◽  
Reproductive Number ◽  
Basic Properties ◽  
Vector Borne Disease ◽  
Vector Population ◽  
Host Type ◽  
Analytical Results ◽  
Vector Borne ◽  
Qualitative Dynamics

This work systematically discusses basic properties and qualitative dynamics of vector-borne disease models, particularly those with vertical transmission in the vector population. Examples of disease include Dengue and Rift Valley fever which are endemic in Sub-Saharan Africa, and understanding of the dynamics underlying their transmission is central for providing critical informative indicators useful for guiding control strategies. Of particular interest is the applicability and derivation of relevant population and epidemic thresholds and their relationships with vertical infection. This study demonstrates how the failure of R0 derived using the next-generation method compounds itself when varying vertical transmission efficiency, and it shows that the host type reproductive number gives the correct R0. Further, novel relationships between the host type reproductive number, vertical infection, and ratio of female mosquitoes to host are established and discussed. Analytical results of the model with vector stages show that the quantities Q0, Q0v, and R0c, which represent the vector colonization threshold, the average number of female mosquitoes produced by a single infected mosquito, and effective reproductive number, respectively, provide threshold conditions that determine the establishment of the vector population and invasion of the disease. Numerical simulations are also conducted to confirm and extend the analytical results. The findings imply that while vertical infection increases the size of an epidemic, it reduces its duration, and control efforts aimed at reducing the critical thresholds Q0, Q0v, and R0c to below unity are viable control strategies.

OPTIMAL CONTROL OF VECTOR-BORNE DISEASE WITH DIRECT TRANSMISSION

2015 ◽  
Vol 76 (13) ◽  
Author(s):  
Nurul Aida Nordin ◽  
Rohanin Ahmad ◽  
Rashidah Ahmad
Keyword(s):  
Dynamical System ◽  
Optimal Control ◽  
Optimal Control Theory ◽  
Existence And Uniqueness ◽  
Blood Donation ◽  
Direct Transmission ◽  
Vector Borne Disease ◽  
Indirect Transmission ◽  
Vector Borne ◽  
Vector Control Strategy

This paper introduces the usage of three controls as a way to reduce the occurrence of vector-borne disease. The governing equation of the dynamical system used in this paper describes both direct and indirect transmission mode of vector-borne disease. This means that the disease can be transmitted in two different ways. First, it can be transmitted through mosquito bites and the other is through human blood transfusion. The three controls that are incorporated in the dynamical system include a measurement of basic practice for blood donation procedure, self-prevention effort and vector control strategy by health authority. The optimality system of the three controls is characterized using optimal control theory and the existence and uniqueness of the optimal control are established. Then, the effect of the incorporation of the three controls is investigated by performing numerical simulation. 

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.

PREVENTING THE SPREAD OF SCHISTOSOMIASIS IN GHANA: POSSIBLE OUTCOMES OF INTEGRATED OPTIMAL CONTROL STRATEGIES

2017 ◽  
Vol 25 (04) ◽  
pp. 625-655 ◽  
Author(s):  
HONG ZHANG ◽  
PRINCE HARVIM ◽  
PAUL GEORGESCU
Keyword(s):  
Optimal Control ◽  
Large Scale ◽  
Control Strategies ◽  
Endemic Equilibrium ◽  
Control Measures ◽  
Dimensional System ◽  
Vector Population ◽  
Sanitation And Hygiene ◽  
The Stability ◽  
Manifold Theory

The goal of a future free from schistosomiasis in Ghana can be achieved through integrated strategies, targeting simultaneously several stages of the life cycle of the schistosome parasite. In this paper, the transmission of schistosomiasis is modeled as a multi-scale 12-dimensional system of ODEs that includes vector-host and within-host dynamics of infection. An explicit expression for the basic reproduction number [Formula: see text] is obtained via the next generation method, this expression being interpreted in biological terms, as well as in terms of reproductive numbers for each type of interaction involved. After discussing the stability of the disease-free equilibrium and the existence and uniqueness of the endemic equilibrium, the Center Manifold Theory is used to show that for values of [Formula: see text] larger than 1, but close to 1, the unique endemic equilibrium is locally asymptotically stable. A sensitivity analysis indicates that [Formula: see text] is most sensitive to the natural death rate of the vector population, while numerical simulations of optimal control strategies reveal that the most effective strategy for the control and possible elimination of schistosomiasis should combine sanitary measures (access to safe water, improved sanitation and hygiene education), large-scale treatment of infected population and vector control measures (via the use of molluscicides), for a significant amount of time.

scholarly journals AN IMMUNO-EPIDEMIOLOGICAL VECTOR–HOST MODEL WITH WITHIN-VECTOR VIRAL KINETICS

2020 ◽  
Vol 28 (02) ◽  
pp. 233-275 ◽  
Author(s):  
HAYRIYE GULBUDAK
Keyword(s):  
Immune Response ◽  
Disease Modeling ◽  
Control Strategies ◽  
Inoculum Size ◽  
Disease Spread ◽  
Positive Equilibrium ◽  
Asymptotically Stable ◽  
Response Dynamics ◽  
Viral Kinetics ◽  
Vector Borne Diseases

A current challenge for disease modeling and public health is understanding pathogen dynamics across scales since their ecology and evolution ultimately operate on several coupled scales. This is particularly true for vector-borne diseases, where within-vector, within-host, and between vector–host populations all play crucial roles in diversity and distribution of the pathogen. Despite recent modeling efforts to determine the effect of within-host virus-immune response dynamics on between-host transmission, the role of within-vector viral dynamics on disease spread is overlooked. Here, we formulate an age-since-infection-structured epidemic model coupled to nonlinear ordinary differential equations describing within-host immune-virus dynamics and within-vector viral kinetics, with feedbacks across these scales. We first define the within-host viral-immune response and within-vector viral kinetics-dependent basic reproduction number [Formula: see text] Then we prove that whenever [Formula: see text] the disease-free equilibrium is locally asymptotically stable, and under certain biologically interpretable conditions, globally asymptotically stable. Otherwise, if [Formula: see text] it is unstable and the system has a unique positive endemic equilibrium. In the special case of constant vector to host inoculum size, we show the positive equilibrium is locally asymptotically stable and the disease is weakly uniformly persistent. Furthermore, numerical results suggest that within-vector-viral kinetics and dynamic inoculum size may play a substantial role in epidemics. Finally, we address how the model can be utilized to better predict the success of control strategies such as vaccination and drug treatment.

scholarly journals Practical unidentifiability of a simple vector-borne disease model: implications for parameter estimation and intervention assessment

2017 ◽  
Author(s):  
Yu-Han Kao ◽  
Marisa C. Eisenberg
Keyword(s):  
Parameter Estimation ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Disease Incidence ◽  
Environmental Drivers ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Vector Borne Disease ◽  
Vector Borne ◽  
The Basic Reproduction Number

AbstractBackgroundMathematical modeling has an extensive history in vector-borne disease epidemiology, and is increasingly used for prediction, intervention design, and understanding mechanisms. Many of these studies rely on parameter estimation to link models and data, and to tailor predictions and counterfactuals to specific settings. However, few studies have formally evaluated whether vector-borne disease models can properly estimate the parameters of interest given the constraints of a particular dataset.Methodology/Principle FindingsIdentifiability methods allow us to examine whether model parameters can be estimated uniquely—a lack of consideration of such issues can result in misleading or incorrect parameter estimates and model predictions. Here, we evaluate both structural (theoretical) and practical identifiability of a commonly used compartmental model of mosquitoborne disease, using 2010 dengue epidemic in Taiwan as a case study. We show that while the model is structurally identifiable, it is practically unidentifiable under a range of human and mosquito time series measurement scenarios. In particular, the transmission parameters form a practically identifiable combination and thus cannot be estimated separately, which can lead to incorrect predictions of the effects of interventions. However, in spite of unidentifiability of the individual parameters, the basic reproduction number was successfully estimated across the unidentifiable parameter ranges. These identifiability issues can be resolved by directly measuring several additional human and mosquito life-cycle parameters both experimentally and in the field.ConclusionsWhile we only consider the simplest case for the model, without explicit environmental drivers, we show that a commonly used model of vector-borne disease is unidentifiable from human and mosquito incidence data, making it difficult or impossible to estimate parameters or assess intervention strategies. This work illustrates the importance of examining identifiability when linking models with data to make predictions, and particularly highlights the importance of combining experimental, field, and case data if we are to successfully estimate epidemiological and ecological parameters using models.Author SummaryMathematical models have seen increasing use in understanding transmission processes, developing interventions, and predicting disease incidence and prevalence. Vector-borne diseases in particular present both a challenge and an opportunity for modeling, due to the complex interactions between host and vector species. A key step in many of these studies is connecting transmission models with data to infer parameters and make useful predictions, which requires careful consideration of identifiability and uncertainty of the model parameters. Whether due to intrinsic limitations of the model structure, or practical limitations of the data collected, is common that many different parameter values may yield the same or very similar fits to the data, making it impossible to successfully estimate the parameters. This issue of parameter unidentifiability can have broad implications for our ability to draw conclusions from mechanistic models—in some cases making it difficult or impossible to generate specific predictions, forecasts, or parameter estimates from a given model and data. Here, we evaluate these questions for a commonly-used model of vectorborne disease, examining how parameter uncertainty and unidentifiability can affect intervention predictions, estimation of the basic reproduction number, and other public health conclusions drawn from the model.

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