Global behavior of SIS epidemic models with age structure and spatial heterogeneity

Kuniya, Toshikazu; Inaba, Hisashi; Yang, Junyuan

doi:10.1007/s13160-018-0300-5

Cited by 14 publications

(11 citation statements)

References 34 publications

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“…( 2020a ), Kuniya and Inaba ( 2013 ), Kuniya ( 2014 ), Kuniya and Iannelli ( 2014 ), Kuniya et al. ( 2016 , 2018 ), Thieme ( 1991 ), and Webb ( 1984 ). Since the model is independent of the location, most studies focused on the temporal dynamics of these models.…”

Section: Introductionmentioning

confidence: 99%

“…( 1994 , 1996 ), Kim ( 2006 ), Kubo and Langlais ( 1994 ), Kuniya et al. ( 2018 ), Kuniya and Oizumi ( 2015 ), Chekroun and Kuniya ( 2020 ), Langlais and Busenberg ( 1997 ), and the references cited therein. In these studies, the classical Laplace diffusion was used to describe the random walk of the host in a connected domain.…”

Section: Introductionmentioning

confidence: 99%

“…Various age-structured epidemic models with Laplace diffusion related to model ( 1.6 ) have been proposed and studied, see Di Blasio ( 2010 ), Kim ( 2006 ), Kubo and Langlais ( 1994 ), Kuniya et al. ( 2018 ), Chekroun and Kuniya ( 2020 ), Kuniya and Oizumi ( 2015 ), Langlais and Busenberg ( 1997 ), and the references cited therein. However, due to their complex structures, the spatial-temporal dynamics of this kind of epidemic models are not well-understood.…”

Section: Introductionmentioning

confidence: 99%

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Mathematical analysis on an age-structured SIS epidemic model with nonlocal diffusion

Kang

Ruan

2021

J. Math. Biol.

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In this paper we propose an age-structured susceptible-infectious-susceptible epidemic model with nonlocal (convolution) diffusion to describe the geographic spread of infectious diseases via long-distance travel. We analyze the well-posedness of the model, investigate the existence and uniqueness of the nontrivial steady state corresponding to an endemic state, and study the local and global stability of this nontrivial steady state. Moreover, we discuss the asymptotic properties of the principal eigenvalue and nontrivial steady state with respect to the nonlocal diffusion rate. The analysis is carried out by using the theory of semigroups and the method of monotone and positive operators. The spectral radius of a positive linear operator associated to the solution flow of the model is identified as a threshold.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Mathematical analysis on an age-structured SIS epidemic model with nonlocal diffusion

Kang

Ruan

2021

J. Math. Biol.

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“…Following that, some manuscripts on the mathematical model of Japanese encephalitis infection were produced, including [3,5,9,10]. Likewise, mathematical frameworks have been generally used to quantify the transmission of different infectious infections, such as, [2,4,7,11,12,14,33,34]. These models are compartmental models where a population is separated into various compartments relating to the various courses of infection.…”

Section: Introductionmentioning

confidence: 99%

The impact of time delay in the transmission of Japanese encephalitis without vaccination

Baniya

Keval

2021

Proyecciones (Antofagasta)

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In the manuscript, the influence of time delay on the transmission of Japanese encephalitis model without vaccination model has been studied. The time delay is because of the existence of an incubation period during which the JE virus reproduces enough in the mosquitoes with the goal that it tends to be transmitted by the mosquitoes to people. The motivation behind this manuscript is to assess the influence of the time delay it takes to infect susceptible human populations after interacting with infected mosquitoes. The steady-states and the threshold value R0 of the delay model were resolved. This value assists with setting up the circumstance that ensure the asymptotic stability of relating equilibrium points. Utilizing the delay as a bifurcation parameter, we built up the circumstance for the presence of a ”Hopf bifurcation”. Moreover, we infer an express equation to decide the stability and direction of ”Hopf bifurcation” at endemic equilibrium by using center manifold theory and normal structure strategy. It has been seen that delay plays a vital role in stability exchanging. In addition, larger values of virus transmission rate from an infected mosquito to susceptible individuals and the natural mortality of humans of a model affect the existence of ”Hopf bifurcation”. Finally, to understand some analytical outcomes, the delay framework is simulated numerically.

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“…They incorporated the heterogeneities of host populations as state variables, including age, stage, size [ 8 ], infection threshold [ 7 ], and resistant hosts [ 6 ]. Some other researchers have focused on epidemic models with spatial heterogeneities [ 9 , 10 , 11 ]. They utilized a patch structure where an epidemic system was divided into a number of patches to represent different spatial characteristics.…”

Section: Introductionmentioning

confidence: 99%

Matrix-Based Formulation of Heterogeneous Individual-Based Models of Infectious Diseases: Using SARS Epidemic as a Case Study

Duan

2021

IJERPH

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Heterogeneities of individual attributes and behaviors play an important role in the complex process of epidemic spreading. Compared to differential equation-based system dynamical models of infectious disease transmission, individual-based epidemic models exhibit the advantage of providing a more detailed description of realities to capture heterogeneities across a population. However, the higher granularity and resolution of individual-based epidemic models comes with the cost of increased computational complexities, which result in difficulty in formulating individual-based epidemic models with mathematics. Furthermore, it requires great effort to understand and reproduce existing individual-based epidemic models presented by previous researchers. We proposed a mathematical formulation of heterogeneous individual-based epidemic models using matrices. Matrices and vectors were applied to represent individual attributes and behaviors. We derived analytical results from the matrix-based formulations of individual epidemic models, and then designed algorithms to force the computation of matrix-based individual epidemic models. Finally, we used a SARS epidemic control as a case study to verify the matrix-based formulation of heterogeneous individual-based epidemic models.

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Global behavior of SIS epidemic models with age structure and spatial heterogeneity

Cited by 14 publications

References 34 publications

Mathematical analysis on an age-structured SIS epidemic model with nonlocal diffusion

Mathematical analysis on an age-structured SIS epidemic model with nonlocal diffusion

The impact of time delay in the transmission of Japanese encephalitis without vaccination

Matrix-Based Formulation of Heterogeneous Individual-Based Models of Infectious Diseases: Using SARS Epidemic as a Case Study

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