Mathematical analysis of a power-law form time dependent vector-borne disease transmission model

Sardar, Tridip; Saha, Bapi

doi:10.1016/j.mbs.2017.03.004

Cited by 19 publications

(21 citation statements)

References 29 publications

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“…The spatial epidemic models have also been applied to vector-borne diseases. For instance, in the studies of dengue ( Delmelle et al, 2016 ; Sardar & Saha, 2017 ; Vincenti-Gonzalez et al, 2017 ), West Nile ( Crowder et al, 2013 ; Harrigan et al, 2014 ; Lin & Zhu, 2017 ), and Zika ( Fitzgibbon, Morgan & Webb, 2017 ), different modeling approaches were used. In the study of the dengue virus, a power-law form time-dependent transmission kernel ( Sardar & Saha, 2017 ), hot-spot detection and risk factor analysis ( Vincenti-Gonzalez et al, 2017 ), and geographically weighted regression model ( Delmelle et al, 2016 ) were used to illustrate how the virus spreads.…”

Section: Resultsmentioning

confidence: 99%

“…For instance, in the studies of dengue ( Delmelle et al, 2016 ; Sardar & Saha, 2017 ; Vincenti-Gonzalez et al, 2017 ), West Nile ( Crowder et al, 2013 ; Harrigan et al, 2014 ; Lin & Zhu, 2017 ), and Zika ( Fitzgibbon, Morgan & Webb, 2017 ), different modeling approaches were used. In the study of the dengue virus, a power-law form time-dependent transmission kernel ( Sardar & Saha, 2017 ), hot-spot detection and risk factor analysis ( Vincenti-Gonzalez et al, 2017 ), and geographically weighted regression model ( Delmelle et al, 2016 ) were used to illustrate how the virus spreads. In the West Nile virus study, a weighted ensemble model ( Harrigan et al, 2014 ) and a spatially explicit model incorporating land-use and climate variables ( Crowder et al, 2013 ) as well as a reaction–diffusion model using a spatial–temporal risk index ( Lin & Zhu, 2017 ) were constructed to explain the spatial diffusion of the virus under different circumstances.…”

Section: Resultsmentioning

confidence: 99%

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Dynamics of Zika virus outbreaks: an overview of mathematical modeling approaches

Wiratsudakul

Suparit

Modchang

2018

PeerJ

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BackgroundThe Zika virus was first discovered in 1947. It was neglected until a major outbreak occurred on Yap Island, Micronesia, in 2007. Teratogenic effects resulting in microcephaly in newborn infants is the greatest public health threat. In 2016, the Zika virus epidemic was declared as a Public Health Emergency of International Concern (PHEIC). Consequently, mathematical models were constructed to explicitly elucidate related transmission dynamics.Survey MethodologyIn this review article, two steps of journal article searching were performed. First, we attempted to identify mathematical models previously applied to the study of vector-borne diseases using the search terms “dynamics,” “mathematical model,” “modeling,” and “vector-borne” together with the names of vector-borne diseases including chikungunya, dengue, malaria, West Nile, and Zika. Then the identified types of model were further investigated. Second, we narrowed down our survey to focus on only Zika virus research. The terms we searched for were “compartmental,” “spatial,” “metapopulation,” “network,” “individual-based,” “agent-based” AND “Zika.” All relevant studies were included regardless of the year of publication. We have collected research articles that were published before August 2017 based on our search criteria. In this publication survey, we explored the Google Scholar and PubMed databases.ResultsWe found five basic model architectures previously applied to vector-borne virus studies, particularly in Zika virus simulations. These include compartmental, spatial, metapopulation, network, and individual-based models. We found that Zika models carried out for early epidemics were mostly fit into compartmental structures and were less complicated compared to the more recent ones. Simple models are still commonly used for the timely assessment of epidemics. Nevertheless, due to the availability of large-scale real-world data and computational power, recently there has been growing interest in more complex modeling frameworks.DiscussionMathematical models are employed to explore and predict how an infectious disease spreads in the real world, evaluate the disease importation risk, and assess the effectiveness of intervention strategies. As the trends in modeling of infectious diseases have been shifting towards data-driven approaches, simple and complex models should be exploited differently. Simple models can be produced in a timely fashion to provide an estimation of the possible impacts. In contrast, complex models integrating real-world data require more time to develop but are far more realistic. The preparation of complicated modeling frameworks prior to the outbreaks is recommended, including the case of future Zika epidemic preparation.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Dynamics of Zika virus outbreaks: an overview of mathematical modeling approaches

Wiratsudakul

Suparit

Modchang

2018

PeerJ

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“…We used Delayed Rejection Adaptive Metropolis algorithm [34] to generate the 95% confidence region. An explanation of this technique for model fitting is given in [35] . The estimated parameters are given in Table 2 the estimated values of unknown initial conditions are given by Table 3 .…”

Section: Model Calibration and Covid-19 Data Sourcementioning

confidence: 99%

Occurrence of backward bifurcation and prediction of disease transmission with imperfect lockdown: A case study on COVID-19

Nadim

Chattopadhyay

2020

Chaos, Solitons & Fractals

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Highlights A new mathematical model on COVID-19 that incorporates imperfect lockdown effect. Backward bifurcation occurs in COVID-19 transmission dynamics cause by imperfect nature of the lockdown efficacy. Under which backward bifurcation does not occur have been identified. Several model parameters as well as the basic reproduction number are estimated. The epidemic trend of COVID-19 in India, Mexico, South Africa and Argentina are predicted by our proposed model.

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“…A combined study of dengue and chikungunya dynamical models have been formulated and analyzed in [18]. There are many mathematical models available in the literature that characterized the dynamics of different vector-borne infections [19][20][21][22][23][24]. The implementation of mathematical modeling approach to the transmission patterns of the novel COVID-19 pandemic is recently studied in [25,26].…”

Section: Introductionmentioning

confidence: 99%

Optimal control analysis of vector-host model with saturated treatment

et al. 2020

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Vector-host infectious diseases remain a challenging issue and cause millions of deaths each year globally. In such outbreaks, many countries especially developing or underdevelopment faces a situation where the number of infected individuals is getting larger and the medical facilities are limited. In this paper, we construct an epidemic model to explore the transmission dynamics of vector-borne diseases with nonlinear saturated incidence rate and saturated treatment function. This type of incidence rate, as well as the saturated treatment function, is also known as the Holling type II form and describes the effect of delayed treatment. Initially, we formulate a mathematical model and then present the basic analysis of the model including the positivity and boundedness of the solution. The threshold quantity R 0 is presented and the stability analysis of the system is carried out for the model equilibria. The global stability results are shown using the Lyapunov function of Goh-Voltera type. The existence of backward bifurcation is discussed using the central manifold theory. Further, the global sensitivity analysis of the model is carried out using the Latin Hypercube sampling and the partial rank correlation coefficient techniques. Moreover, an optimal control problem is formulated and the necessary optimality conditions are investigated in order to eradicate the disease in a community. Four strategies are presented by choosing different set of controls combination for the disease minimization. Finally, the numerical simulations of each strategy are depicted to demonstrate the importance of suggesting control interventions on the disease dynamics and eradication.

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Mathematical analysis of a power-law form time dependent vector-borne disease transmission model

Cited by 19 publications

References 29 publications

Dynamics of Zika virus outbreaks: an overview of mathematical modeling approaches

Dynamics of Zika virus outbreaks: an overview of mathematical modeling approaches

Occurrence of backward bifurcation and prediction of disease transmission with imperfect lockdown: A case study on COVID-19

Optimal control analysis of vector-host model with saturated treatment

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