Optimal control and basic reproduction numbers for a compartmental spatial multipatch dengue model

Böck, Wolfgang; Jayathunga, Yashika

doi:10.1002/mma.4812

Cited by 25 publications

(21 citation statements)

References 30 publications

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“…However, the data availability is limited for the factors like human mobility. It would be purposeful to moderate the developed model to a spatial model by incorporating human mobility in further research [ 45 , 49 , 50 ].…”

Section: Discussionmentioning

confidence: 99%

Analysis and forecast of dengue incidence in urban Colombo, Sri Lanka

Erandi

Perera

Mahasinghe

2021

Theor Biol Med Model

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Background Understanding the dynamical behavior of dengue transmission is essential in designing control strategies. Mathematical models have become an important tool in describing the dynamics of a vector borne disease. Classical compartmental models are well–known method used to identify the dynamical behavior of spread of a vector borne disease. Due to use of fixed model parameters, the results of classical compartmental models do not match realistic nature. The aim of this study is to introduce time in varying model parameters, modify the classical compartmental model by improving its predictability power. Results In this study, per–capita vector density has been chosen as the time in varying model parameter. The dengue incidences, rainfall and temperature data in urban Colombo are analyzed using Fourier mathematical analysis tool. Further, periodic pattern of the reported dengue incidences and meteorological data and correlation of dengue incidences with meteorological data are identified to determine climate data–driven per–capita vector density parameter function. By considering that the vector dynamics occurs in faster time scale compares to host dynamics, a two dimensional data–driven compartmental model is derived with aid of classical compartmental models. Moreover, a function for per–capita vector density is introduced to capture the seasonal pattern of the disease according to the effect of climate factors in urban Colombo. Conclusions The two dimensional data–driven compartmental model can be used to predict weekly dengue incidences upto 4 weeks. Accuracy of the model is evaluated using relative error function and the model can be used to predict more than 75% accurate data.

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Section: Discussionmentioning

confidence: 99%

Analysis and forecast of dengue incidence in urban Colombo, Sri Lanka

Erandi

Perera

Mahasinghe

2021

Theor Biol Med Model

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“…It is important to note that , where m ij ∈ [0, 1]. The term m ij in residence-time budgeting matrix refers to the fraction of time spent in another patch [17]. Based on the commuting matrix for Rhineland-Palatinate, hence the average mobility behaviour within the state, the matrix M can be deduced, by assuming that an individual spends 1 / 3 of the day at work (at the state it commutes to if not working in its residing state) and 2 / 3 of the day in its residing state.…”

Section: Methodsmentioning

confidence: 99%

Are the upper bounds for new SARS-CoV-2 infections in Germany useful?

Böck¹,

Goetz

Jayathunga

et al. 2020

Preprint

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At the end of 2019, an outbreak of a new coronavirus, called SARS--CoV--2, was reported in China and later in other parts of the world. First infections were reported in Germany by the end of January and on March 16th the federal government announced a partial lockdown in order to mitigate the spread. Since the dynamics of new infections started to slow down, German states started to relax the confinement measures as to the beginning of May. As a fall back option, a limit of 50 new infections per 100,000 inhabitants within seven days was introduced for each city or district in Germany. If a district exceeds this limit, measures to control the spread of the virus should be taken. Based on a multi--patch SEAIRD--type model, we will simulate the effect of choosing a specific upper limit for new infections. We investigate, whether the politically motivated bound is low enough to detect new outbreaks at an early stage. Subsequently, we introduce an optimal control problem to tackle the multi--criteria problem of finding a bound for new infections that is low enough to avoid new outbreaks, which might lead to an overload of the health care system, but is large enough to curb the expected economic losses.

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“…It follows that the basic reproduction number of the model, Equation (3), denoted by R 0 , is given by R 0 = ρ(FV −1 ), where ρ is the spectral radius (maximum eigenvalues) [15,18]. Hence,…”

Section: Stability Of the Disease-free Equilibrium (Dfe)mentioning

confidence: 99%

Qualitative Analysis of a Dengue Fever Model

Gbadamosi

Ojo

Oke

et al. 2018

MCA

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In this paper, a deterministic mathematical model of the Dengue virus with a nonlinear incidence function in a population is presented and rigorously analysed. The model incorporates control measures at the aquatic and adult stages of the vector (mosquito). The stability of the system is analysed for the disease-free equilibrium and the existence of endemic equilibria under certain conditions. The local stability of the Dengue-free equilibrium is investigated via the threshold parameter (reproduction number) that was obtained using the next-generation matrix techniques. The Routh-Hurwitz criterion, along with Descartes' rule of signs change, established the local asymptotically stability of the model whenever R 0 < 1 and was unstable otherwise. The comparison theorem was used to establish the global asymptomatically stability of the model.

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Optimal control and basic reproduction numbers for a compartmental spatial multipatch dengue model

Cited by 25 publications

References 30 publications

Analysis and forecast of dengue incidence in urban Colombo, Sri Lanka

Analysis and forecast of dengue incidence in urban Colombo, Sri Lanka

Are the upper bounds for new SARS-CoV-2 infections in Germany useful?

Qualitative Analysis of a Dengue Fever Model

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