Mathematical Study of Dengue Disease Transmission in Multi-Patch Environment

Phaijoo, Ganga Ram; Gurung, Dil Bahadur

doi:10.4236/am.2016.714132

Cited by 25 publications

(19 citation statements)

References 15 publications

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“…Dynamics of malaria disease was studied in patchy environment by Auger et al They generalized Ross-Macdonald model to n -patches to describe the transmission dynamics of the disease [ 24 ]. Lee and Castillo-Chavez [ 25 ] and Phaijoo and Gurung [ 26 ] discussed dengue disease transmission dynamics in patchy environment.…”

Section: Introductionmentioning

confidence: 99%

Modeling Impact of Temperature and Human Movement on the Persistence of Dengue Disease

Phaijoo

Gurung

2017

Computational and Mathematical Methods in Medicine

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Dengue is a vector-borne infectious disease endemic in many parts of the world. The disease is spreading in new places due to human movement into the dengue disease supporting areas. Temperature is the major climatic factor which affects the biological processes of the mosquitoes and their interaction with the viruses. In the present work, we propose a multipatch model to assess the impact of temperature and human movement in the transmission dynamics of dengue disease. The work consists of system of ordinary differential equations that describe the transmission dynamics of dengue disease between humans and mosquitoes. Human population is divided into four classes: susceptible, exposed, infectious, and recovered. Mosquito population is divided into three classes: susceptible, exposed, and infectious. Basic reproduction number ℛ0 of the model is obtained using Next-Generation Matrix method. The qualitative analysis of the model is made in terms of the basic reproduction number. Parameters used in the model are considered temperature dependent. Dynamics of vector and host populations are investigated with different human movement rates and different temperature levels. Numerical results show that proper management of human movement between patches helps reducing the burden of dengue disease. It is also seen that the temperature affects the transmission dynamics of the disease significantly.

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Section: Introductionmentioning

confidence: 99%

Modeling Impact of Temperature and Human Movement on the Persistence of Dengue Disease

Phaijoo

Gurung

2017

Computational and Mathematical Methods in Medicine

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“…Under these assumptions they derive the epidemic threshold and an indicator allowing to measure the risk for the patches to be affected by the disease. In order to study the dynamics of Dengue, Phaijoo and Gurung [43] proposed a multi-patch SIR-SI model where individuals can migrate to different patches. The disease prevalence is assumed to be variable for the different patches and the mobility rate between patches is also variable in their model.…”

Section: A Influence Of Environmental Factors On Vector-borne Diseasesmentioning

confidence: 99%

Impact of Seasonal Conditions on Vector-Borne Epidemiological Dynamics

2020

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Vector-borne diseases such as malaria, dengue fever, West Nile virus, and so forth are some of the most prominent threats to human health. They are transmitted to the human population by infected insects or by direct transmission between humans. The epidemic process relies on suitable environmental and climatic conditions. Indeed, climatic factors affect the development of pathogens in vectors as well as the population dynamics of the vectors impacting significantly the incidence of disease in the human population. While the influence of the climatic conditions on Vector-borne diseases is well-documented, there is a strong need to design more realistic epidemiological models incorporating environmental features that show a close relationship with the epidemic process observed in the human population. Indeed, classical models concentrate either on the climatic influence on the vector population dynamics or on the connectivity patterns of the host population, loosing the full picture of the epidemic process dynamics. Inspired by real data of infectious diseases, a Seasonal Susceptible-Infected-Recovered (Seasonal SIR) epidemiological model is developed and analyzed. The proposed model incorporates the influence of the temperature variations together with the heterogeneous structure of the human interaction network on the spreading process of vector-borne diseases. Simulations are performed in order to get a better understanding of the climate variations and of the heterogeneous nature of the contact network on the transmission dynamics. Results show that failing to incorporate these features on the model can lead to a poor estimation of the maximum fraction of infected individuals in the host population. Furthermore there is a serious influence on the time needed to reach this maximum. The Seasonal SIR model proves to finely model the dynamics of outbreaks observed in real-world situations. It provides a basis for more effective predictions of disease outbreaks that can be used in order to implement appropriate control measures to contain epidemics. INDEX TERMS Vector-borne diseases, epidemics, heterogeneous contact network, climate variations, dynamics on networks, SIR model, epidemiological models.

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“…Most of the works are channeled to different aspects of disease. For examples [8], [13], [16], [20] and [23] all developed an SIR epidemic model to show the mode of transmission of dengue disease considering both the human and mosquito population in their work. [6,7] developed an SEIR model to determine the influence of climatic condition such as rainfall on mode of transmission of dengue in Thailand.…”

Section: Many Mathematical Models Have Been Put In Place To Describe mentioning

confidence: 99%

“…Also in 2016, [13] studied looked into the model of transmission with and without awareness campaign, where they made the assumption that in the case of awareness, that the humans population protects themselves against the infected mosquitor, (that is, they avoid the bite of mosquitoes by sleeping under net maybe). While on the other case of non-awareness there is a bite of human by the mosquitoes.…”

Section: Many Mathematical Models Have Been Put In Place To Describe mentioning

confidence: 99%

Mathematical Model of the Transmission Dynamics of Dengue Fever in Two Categories with Vaccination and Migration Effect

2020

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A. In this study, we propose an SIR Mathematical model with vaccination and migration effect to analyze the behaviours of the transaction of Dengue when vaccination with dengvaxia has been carried out. There is no effective of Dengue disease. We introduce check and vaccination of immigrants as a measure in the model which can help to reduce the burden of Dengue disease. Basic reproduction number was calculated and used to determine whether the disease comes under control when R < 1 and become more prevalent when R > 1. Results in the work showed that disease-free equilibrium of the model is locally asymptotically stabe and the endemic equilibrium was proved to be globally asymptotically stable when R < 1 using Lyapunov method. To understand more of the model we illustrate that with aid of simulation and from the first simulation it was revealed that the susceptibles mosqutoes remains in the population, when the susceptible mosquitoes bites any of the class which results in the spread of Dengue disease. The second simulation reveals that the population will be reduced over time, that is to say that for a period of 555 days the entire severely infected will go into extenction when q 1 = q 2 = 0. Simulation also shows that with vaccination alone, the severely infected population can be reduced but can not be wiped out on the long run.

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Mathematical Study of Dengue Disease Transmission in Multi-Patch Environment

Cited by 25 publications

References 15 publications

Modeling Impact of Temperature and Human Movement on the Persistence of Dengue Disease

Modeling Impact of Temperature and Human Movement on the Persistence of Dengue Disease

Impact of Seasonal Conditions on Vector-Borne Epidemiological Dynamics

Mathematical Model of the Transmission Dynamics of Dengue Fever in Two Categories with Vaccination and Migration Effect

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