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

Kang, Hao; Ruan, Shigui

doi:10.1007/s00285-021-01634-x

Cited by 20 publications

(11 citation statements)

References 42 publications

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“…Here, we found the counterintuitive result that under a strict one-child policy, increasing a min first increases the stationary net growth rate, before decreasing it as a min is further increased. Age-structured models can also be generalized to include additional subpopulations, such as those arising in cell division [40] and disease propagation [41] models. For example, in the birth control context, different generations and family structure can be enumerated in order to predict the effects of policies such as those implemented in 2011 and 2014 that consider the sibling status of would-be parents, allowing those without siblings more latitude in childbirth.…”

Section: Discussionmentioning

confidence: 99%

Modelling the impact of birth control policies on China’s population and age: effects of delayed births and minimum birth age constraints

Wang¹,

Dessalles²,

Chou

2022

R. Soc. open sci.

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We consider age-structured models with an imposed refractory period between births. These models can be used to formulate alternative population control strategies to China’s one-child policy. By allowing any number of births, but with an imposed delay between births, we show how the total population can be decreased and how a relatively older age distribution can be generated. This delay represents a more ‘continuous’ form of population management for which the strict one-child policy is a limiting case. Such a policy approach could be more easily accepted by society. Our analyses provide an initial framework for studying demographics and how social constraints influence population structure.

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Section: Discussionmentioning

confidence: 99%

Modelling the impact of birth control policies on China’s population and age: effects of delayed births and minimum birth age constraints

Wang¹,

Dessalles²,

Chou

2022

R. Soc. open sci.

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“…More recent developments include nonlinear models (Liu et al. 2018 ), age-structured model with diffusion (Kang and Ruan 2021 ; Ou and Wu 2006 ) and vaccination (Castillo-Chavez and Feng 1998 ; Müller 1998 ; Shim et al. 2006 ), with age-since-infection (Li et al.…”

Section: Introductionmentioning

confidence: 99%

An age-dependent immuno-epidemiological model with distributed recovery and death rates

2023

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The work is devoted to a new immuno-epidemiological model with distributed recovery and death rates considered as functions of time after the infection onset. Disease transmission rate depends on the intra-subject viral load determined from the immunological submodel. The age-dependent model includes the viral load, recovery and death rates as functions of age considered as a continuous variable. Equations for susceptible, infected, recovered and dead compartments are expressed in terms of the number of newly infected cases. The analysis of the model includes the proof of the existence and uniqueness of solution. Furthermore, it is shown how the model can be reduced to age-dependent SIR or delay model under certain assumptions on recovery and death distributions. Basic reproduction number and final size of epidemic are determined for the reduced models. The model is validated with a COVID-19 case data. Modelling results show that proportion of young age groups can influence the epidemic progression since disease transmission rate for them is higher than for other age groups.

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“…Compared with the local diffusion represented by the Laplacian operator, nonlocal diffusion represents the movement of individuals not limited to one local area but extended to a wider area. Therefore, nonlocal diffusion models can address a larger class of natural phenomena and have recently attracted considerable attention (see Andreu-Vaillo et al [16] and other references [17][18][19][20][21][22][23][24][25][26][27][28][29]).…”

Section: Introductionmentioning

confidence: 99%

Mathematical analysis of a vaccination epidemic model with nonlocal diffusion

Bentout

Djilali

Kuniya

et al. 2023

Math Methods in App Sciences

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We study the global dynamics of a susceptible-vaccinated-infected-recovered model that incorporates nonlocal diffusion. By identifying the basic reproduction number ℛ 0 of the model, we obtain the following threshold-type results: (i) If ℛ 0 < 1, then the epidemic becomes extinct in the sense that the infection-free equilibrium is globally attractive; (ii) if ℛ 0 > 1 and the diffusion coefficients are the same for all classes, then the epidemic persists in the sense that the system is uniformly persistent; and (iii) if ℛ 0 > 1, the diffusion coefficients for susceptible, and the vaccinated classes are zero, then the system admits a unique endemic equilibrium, and the omega-limit set is included in the singleton of the endemic equilibrium. Our results show that ℛ 0 is an essential value for determining global epidemic dynamics in our model.

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

Cited by 20 publications

References 42 publications

Modelling the impact of birth control policies on China’s population and age: effects of delayed births and minimum birth age constraints

Modelling the impact of birth control policies on China’s population and age: effects of delayed births and minimum birth age constraints

An age-dependent immuno-epidemiological model with distributed recovery and death rates

Mathematical analysis of a vaccination epidemic model with nonlocal diffusion

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