MODELING ZIKA TRANSMISSION DYNAMICS: PREVENTION AND CONTROL

2020 ◽  
Vol 28 (03) ◽  
pp. 719-749
Author(s):  
PARIMITA ROY ◽  
RANJIT KUMAR UPADHYAY ◽  
JASMINE CAUR
Keyword(s):  
Optimal Control ◽  
Zika Virus ◽  
Deterministic Model ◽  
Transmission Rate ◽  
Spatial Diversity ◽  
Transmission Dynamics ◽  
Model Parameters ◽  
Human Populations ◽  
Mosquito Vector ◽  
The Impact

The Zika virus (ZIKV) epidemic is depicted to have high spatial diversity and slow growth, attributable to the dynamics of the mosquito vector and mobility of the human populations. In an effort to understand the transmission dynamics of Zika virus, we formulate a new compartmental epidemic model with a system of seven differential equations and 11 parameters incorporating the decaying transmission rate and study the impact of protection measure on basic public health. We do not fit the model to the observed pattern of spread, rather we use parameter values estimated in the past and examine the extent to which the designed model prediction agrees with the pattern of spread seen in Brazil, via reaction–diffusion modeling. Our work includes estimation of key epidemiological parameters such as basic reproduction number ([Formula: see text], and gives a rough estimate of how many individuals can be typically infected during an outbreak if it occurs in India. We used partial rank correlation coefficient method for global sensitivity analysis to identify the most influential model parameters. Using optimal control theory and Pontryagin’s maximum principle, a control model has been proposed and conditions for the optimal control are determined for the deterministic model of Zika virus. The control functions for the strategies (i) vector-to-human contact reduction and (ii) vector elimination are introduced into the system. Numerical simulations are also performed. This work aimed at understanding the potential extent and timing of the ZIKV epidemic can be used as a template for the analysis of future mosquito-borne epidemics.

scholarly journals Analysis of the Model on the Effect of Seasonal Factors on Malaria Transmission Dynamics

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Victor Yiga ◽  
Hasifa Nampala ◽  
Julius Tumwiine
Keyword(s):  
Malaria Transmission ◽  
Basic Reproduction Number ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Current Control ◽  
Transmission Dynamics ◽  
Mosquito Vector ◽  
The Impact ◽  
The Basic Reproduction Number

Malaria is one of the world’s most prevalent epidemics. Current control and eradication efforts are being frustrated by rapid changes in climatic factors such as temperature and rainfall. This study is aimed at assessing the impact of temperature and rainfall abundance on the intensity of malaria transmission. A human host-mosquito vector deterministic model which incorporates temperature and rainfall dependent parameters is formulated. The model is analysed for steady states and their stability. The basic reproduction number is obtained using the next-generation method. It was established that the mosquito population depends on a threshold value θ , defined as the number of mosquitoes produced by a female Anopheles mosquito throughout its lifetime, which is governed by temperature and rainfall. The conditions for the stability of the equilibrium points are investigated, and it is shown that there exists a unique endemic equilibrium which is locally and globally asymptotically stable whenever the basic reproduction number exceeds unity. Numerical simulations show that both temperature and rainfall affect the transmission dynamics of malaria; however, temperature has more influence.

scholarly journals Transmission Dynamics of Hepatitis C with Control Strategies

2014 ◽  
Vol 2014 ◽  
pp. 1-18 ◽  
Author(s):  
Adnan Khan ◽  
Sultan Sial ◽  
Mudassar Imran
Keyword(s):  
Optimal Control ◽  
Hepatitis C ◽  
Deterministic Model ◽  
Control Strategies ◽  
Endemic Equilibrium ◽  
Transmission Dynamics ◽  
Critical Parameters ◽  
Optimal Controls ◽  
Infected Population ◽  
The Impact

We present a rigorous mathematical analysis of a deterministic model, for the transmission dynamics of hepatitis C, using a standard incidence function. The infected population is divided into three distinct compartments featuring two distinct infection stages (acute and chronic) along with an isolation compartment. It is shown that for basic reproduction number R0≤1, the disease-free equilibrium is locally and globally asymptotically stable. The model also has an endemic equilibrium for R0>1. Uncertainty and sensitivity analyses are carried out to identify and study the impact of critical parameters on R0. In addition, we have presented the numerical simulations to investigate the influence of different important parameters on R0. Since we have a locally stable endemic equilibrium, optimal control is applied to the deterministic model to reduce the total infected population. Two different optimal control strategies (vaccination and isolation) are designed to control the disease and reduce the infected population. Pontryagin’s Maximum Principle is used to characterize the optimal controls in terms of an optimality system which is solved numerically. Numerical results for the optimal controls are compared against the constant controls and their effectiveness is discussed.

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.

MODELING THE IMPACT OF VOLUNTARY TESTING AND TREATMENT ON TUBERCULOSIS TRANSMISSION DYNAMICS

2012 ◽  
Vol 05 (04) ◽  
pp. 1250029 ◽  
Author(s):  
S. MUSHAYABASA ◽  
C. P. BHUNU
Keyword(s):  
Deterministic Model ◽  
Reproduction Number ◽  
Positive Impact ◽  
Transmission Dynamics ◽  
Effective Control ◽  
Reproductive Number ◽  
Voluntary Testing ◽  
Manifold Theory ◽  
The Impact ◽  
Disease Free

A deterministic model for evaluating the impact of voluntary testing and treatment on the transmission dynamics of tuberculosis is formulated and analyzed. The epidemiological threshold, known as the reproduction number is derived and qualitatively used to investigate the existence and stability of the associated equilibrium of the model system. The disease-free equilibrium is shown to be locally-asymptotically stable when the reproductive number is less than unity, and unstable if this threshold parameter exceeds unity. It is shown, using the Centre Manifold theory, that the model undergoes the phenomenon of backward bifurcation where the stable disease-free equilibrium co-exists with a stable endemic equilibrium when the associated reproduction number is less than unity. The analysis of the reproduction number suggests that voluntary tuberculosis testing and treatment may lead to effective control of tuberculosis. Furthermore, numerical simulations support the fact that an increase voluntary tuberculosis testing and treatment have a positive impact in controlling the spread of tuberculosis in the community.

Dynamical analysis of a class of hepatitis C virus infection models with application of optimal control

2016 ◽  
Vol 09 (03) ◽  
pp. 1650038 ◽  
Author(s):  
Aida Mojaver ◽  
Hossein Kheiri
Keyword(s):  
Optimal Control ◽  
Hepatitis C Virus ◽  
Hepatitis C ◽  
Deterministic Model ◽  
Treatment Strategies ◽  
Dynamical Analysis ◽  
Existence And Stability ◽  
Direct Cell ◽  
Infected Cells ◽  
The Impact

In this paper, we deal with the problem of optimal control of a deterministic model of hepatitis C virus (HCV). In the first part of our analysis, a mathematical modeling of HCV dynamics which can be controlled by antiretroviral therapy as fixed controls has been presented and analyzed which incorporates two mechanisms: infection by free virions and the direct cell-to-cell transmission. Basic reproduction number is calculated and the existence and stability of equilibria are investigated. In the second part, the optimal control problem representing drug treatment strategies of the model is explored considering control parameters as time-dependent in order to minimize not only the population of infected cells but also the associated costs. At the end of the paper, the impact of combination of the strategies in the control of HCV and their effectiveness are compared by numerical simulation.

Input and Design Optimization Under Uncertainty to Minimize the Impact Velocity of an Electrostatically Actuated MEMS Switch

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
M. S. Allen ◽  
J. E. Massad ◽  
R. V. Field ◽  
C. W. Dyck
Keyword(s):  
Impact Velocity ◽  
Deterministic Model ◽  
Electrostatic Force ◽  
Optimization Under Uncertainty ◽  
Model Parameters ◽  
Rf Switch ◽  
Voltage Waveform ◽  
Rigid Barrier ◽  
Mechanical Impact ◽  
The Impact

The dynamic response of a radio-frequency (RF) microelectromechanical system to a time-varying electrostatic force is optimized to enhance robustness to variations in material properties and geometry. The device functions as an electrical switch, where an applied voltage is used to close a circuit. The objective is to minimize the severity of the mechanical impact that occurs each time the switch closes because severe impacts have been found to significantly decrease the life of these switches. Previous works have demonstrated that a classical vibro-impact model, a single-degree-of-freedom oscillator subject to mechanical impact with a single rigid barrier, captures the relevant physics adequately. Certain model parameters are described as random variables to represent the significant unit-to-unit variability observed during fabrication and testing of a collection of nominally identical switches; these models for unit-to-unit variability are calibrated to available experimental data. Our objective is to design the shape and duration of the voltage waveform so that impact kinetic energy at switch closure is minimized for the collection of nominally identical switches, subject to design constraints. A voltage waveform designed using a deterministic model for the RF switch is found to perform poorly on the ensemble. An alternative waveform is generated using the proposed optimization procedure with a probabilistic model and is found to decrease the maximum impact velocity by a factor of 2 relative to the waveform designed deterministically. The methodology is also applied to evaluate a design change that reduces the impact velocity further and to predict the effect of fabrication process improvements.

scholarly journals Spread of Zika virus in the Americas

2017 ◽  
Vol 114 (22) ◽  
pp. E4334-E4343 ◽  
Author(s):  
Qian Zhang ◽  
Kaiyuan Sun ◽  
Matteo Chinazzi ◽  
Ana Pastore y Piontti ◽  
Natalie E. Dean ◽  
...  
Keyword(s):  
Zika Virus ◽  
Retrospective Studies ◽  
Slow Growth ◽  
Human Mobility ◽  
Credible Interval ◽  
First Trimester ◽  
Human Populations ◽  
Mosquito Vector ◽  
Stochastic Epidemic ◽  
Different Levels

We use a data-driven global stochastic epidemic model to analyze the spread of the Zika virus (ZIKV) in the Americas. The model has high spatial and temporal resolution and integrates real-world demographic, human mobility, socioeconomic, temperature, and vector density data. We estimate that the first introduction of ZIKV to Brazil likely occurred between August 2013 and April 2014 (90% credible interval). We provide simulated epidemic profiles of incident ZIKV infections for several countries in the Americas through February 2017. The ZIKV epidemic is characterized by slow growth and high spatial and seasonal heterogeneity, attributable to the dynamics of the mosquito vector and to the characteristics and mobility of the human populations. We project the expected timing and number of pregnancies infected with ZIKV during the first trimester and provide estimates of microcephaly cases assuming different levels of risk as reported in empirical retrospective studies. Our approach represents a modeling effort aimed at understanding the potential magnitude and timing of the ZIKV epidemic and it can be potentially used as a template for the analysis of future mosquito-borne epidemics.

scholarly journals Modeling the Impact of Optimal Control Strategies on the Dynamics of Zika Virus Disease Using the Sterile Insect Technology

2020 ◽  
pp. 13-33
Author(s):  
Atokolo William ◽  
Akpa Johnson ◽  
Daniel Musa Alih ◽  
Olayemi Kehinde Samuel ◽  
C. E. Mbah Godwin
Keyword(s):  
Optimal Control ◽  
Control Strategy ◽  
Zika Virus ◽  
Human Population ◽  
Necessary Conditions ◽  
Virus Disease ◽  
Control Strategies ◽  
Control Measures ◽  
Optimal Control Strategy ◽  
The Impact

This work is aimed at formulating a mathematical model for the control of zika virus infection using Sterile Insect Technology (SIT). The model is extended to incorporate optimal control strategy by introducing three control measures. The optimal control is aimed at minimizing the number of Exposed human, Infected human and the total number of Mosquitoes in a population and as such reducing contacts between mosquitoes and human, human to human and above all, eliminates the population of Mosquitoes. The Pontryagin’s maximum principle was used to obtain the necessary conditions, find the optimality system of our model and to obtain solution to the control problem. Numerical simulations result shows that; reduction in the number of Exposed human population, Infected human population and reduction in the entire population of Mosquito population is best achieved using the optimal control strategy.

scholarly journals Qualitative behaviour of a stochastic hepatitis C epidemic model in cellular level

2021 ◽  
Vol 19 (2) ◽  
pp. 1515-1535
Author(s):  
Dwi Lestari ◽  
◽  
Noorma Yulia Megawati ◽  
Nanang Susyanto ◽  
Fajar Adi-Kusumo ◽  
...  
Keyword(s):  
Hepatitis C ◽  
Deterministic Model ◽  
Transmission Rate ◽  
Cellular Level ◽  
Stochastic Noise ◽  
Qualitative Behaviour ◽  
Initial Value ◽  
Analysis Techniques ◽  
Model Dynamics ◽  
The Impact

<abstract><p>In this paper, a mathematical model describing the dynamical of the spread of hepatitis C virus (HCV) at a cellular level with a stochastic noise in the transmission rate is developed from the deterministic model. The unique time-global solution for any positive initial value is served. The Ito's Formula, the suitable Lyapunov function, and other stochastic analysis techniques are used to analyze the model dynamics. The numerical simulations are carried out to describe the analytical results. These results highlight the impact of the noise intensity accelerating the extinction of the disease.</p></abstract>

scholarly journals Modeling the impact of early interventions on the transmission dynamics of coronavirus infection

F1000Research ◽  
2021 ◽  
Vol 10 ◽  
pp. 518
Author(s):  
Christopher Saaha Bornaa ◽  
Baba Seidu ◽  
Yakubu Ibrahim Seini
Keyword(s):  
Death Rate ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Transmission Probability ◽  
Transmission Dynamics ◽  
Early Interventions ◽  
Coronavirus Infection ◽  
The Impact ◽  
Disease Free

A deterministic model is proposed to describe the transmission dynamics of coronavirus infection with early interventions. Epidemiological studies have employed modeling to unravel knowledge that transformed the lives of families, communities, nations and the entire globe. The study established the stability of both disease free and endemic equilibria. Stability occurs when the reproduction number, R0, is less than unity for both disease free and endemic equilibrium points. The global stability of the disease-free equilibrium point of the model is established whenever the basic reproduction number R0 is less than or equal to unity. The reproduction number is also shown to be directly related to the transmission probability (β), rate at which latently infected individuals join the infected class (δ) and rate of recruitment (Λ). It is inversely related to natural death rate (μ), rate of early treatment (τ1), rate of hospitalization of infected individuals (θ) and Covid-induced death rate (σ). The analytical results established are confirmed by numerical simulation of the model.

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