A Model for Brucellosis Disease Incorporating Age of Infection and Waning Immunity

Kenne, Cyrille; Mophou, Gisèle; Dorville, René; Zongo, Pascal

doi:10.3390/math10040670

Cited by 5 publications

(5 citation statements)

References 33 publications

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“…Let (S 0 , V 0 , e 0 (τ), I 0 , R 0 ) ∈ ∂B, and we have (e 0 (τ), I 0 , R 0 ) ∈ ∂ B. Then, the following system is obtained: (19) which is subject to the boundary…”

Section: Uniform Persistencementioning

confidence: 99%

“…Dai and Zhang [18] claimed that the incidence of eating disorders could be lowered if people continued their education. Kenne et al [19] demonstrated that birth rates directly affected the stability of diseases and that changing certain parameters triggered periodic epidemics, making it difficult to eradicate them from the population. Li and Wang [20] held that in order to effectively control infectious diseases, it was crucial to recruit few susceptible people, restrict travel, and ban large gatherings of people, in addition to vaccination.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dynamical Analysis of an Age-Structured SVEIR Model with Imperfect Vaccine

Wang

Zhang

2023

Mathematics

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Based on the spread of COVID-19, in the present paper, an imperfectly vaccinated SVEIR model for latent age is proposed. At first, the equilibrium points and the basic reproduction number of the model are calculated. Then, we discuss the asymptotic smoothness and uniform persistence of the semiflow generated by the solutions of the system and the existence of an attractor. Moreover, LaSalle’s invariance principle and Volterra type Lyapunov functions are used to prove the global asymptotic stability of both the disease-free equilibrium and the endemic equilibrium of the model. The conclusion is that if the basic reproduction number Rρ is less than one, the disease will gradually disappear. However, if the number is greater than one, the disease will become endemic and persist. In addition, numerical simulations are also carried out to verify the result. Finally, suggestions are made on the measures to control the ongoing transmission of COVID-19.

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“…Let (S 0 , V 0 , e 0 (τ), I 0 , R 0 ) ∈ ∂B, and we have (e 0 (τ), I 0 , R 0 ) ∈ ∂ B. Then, the following system is obtained: (19) which is subject to the boundary…”

Section: Uniform Persistencementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamical Analysis of an Age-Structured SVEIR Model with Imperfect Vaccine

Wang

Zhang

2023

Mathematics

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“…Brucellosis in the exposure period is hardly detected, and animals in this period can also infect susceptible animal and humans. Hence, we ignored the exposed/latent period in both human and animal population (see for example [15,20,21,22]);…”

Section: An Autonomous Brucellosis Modelmentioning

confidence: 99%

“…Several mathematical models have been proposed to study the dynamics of brucellosis outbreaks [5,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26]. Undeniably, these studies have produced many useful results and improved the existing knowledge on brucellosis dynamics.…”

Section: Introductionmentioning

confidence: 99%

An Intrinsic Analysis of Human Brucellosis Dynamics in Africa

Lolika¹,

Helikumi²

2022

ARJOM

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Brucellosis is one of the most common zoonotic infections globally. It affects humans, domestic animals and wildlife. In this paper, we conduct an intrinsic analysis of human brucellosis dynamics in non-periodic and periodic environments. As such we propose and study twomathematical models for human brucellosis transmission and control, in which humans acquire infection from cattle and wildlife. The first model is an autonomous dynamical system and the second is a non-autonomous dynamical system in which the seasonal transmission of brucellosisis incorporated. Disease intervention strategies incorporated in this study are cattle vaccination, culling of infectious cattle and human treatment. For both models we conduct both epidemic and endemic analysis, with a focus on the threshold dynamics characterized by the basic reproductionnumbers. Using sensitivity analysis we established that R0 is most sensitive to the rate of brucellosis transmission from buffalos to cattle, the result suggest that in order to control human brucellosis there is a need to control cattle infection. Based on our models, we also formulatean optimal control problem with cattle vaccination and culling of infectious cattle as control functions. Using reasonable parameter values, numerical simulations of the optimal control demonstrate the possibility of reducing brucellosis incidence in humans, wildlife and cattle, withina finite time horizon, for both periodic and non-periodic environments.

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“…Mathematical models have proved to be essential guiding tools for epidemiologists, biologists as well as policy makers (See for example [10,11,12,13,14,15,16,17,18]). Recently, modelling the transmission dynamics of brucellosis, is one of the most common global zoonoses [19], has been an interesting topic for a number of researchers (see, for example [6,18,20,21,22,23,24,25,26,27]).…”

Section: Introductionmentioning

confidence: 99%

Dynamics and Analysis of Chronic Brucellosis in Sheep

Lolika

Helikumi

2022

JAMCS

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We proposed and studied a new fractional-order model for the transmission dynamics of brucellosis with a special focus on the sheep-to-sheep transmission. Two control strategies namely; culling and vaccination rate are incorporated in the model. We computed the basic reproduction number R0 and we studied the global stability of disease-free and endemic equilibrium point in terms of basic reproduction number R0: We found that both the disease-free and endemic equilibrium points are globally stable whenever R0 < 1 and R0 > 1 respectively. In numerical simulations, we performed the sensitivity analysis of the model and expressed the relationship between model parameters and R0:We noted that, increase on the magnitude of model parameters with negative correlation coefficients would significantly reduce the spread of Brucellosis disease in the population. Moreover, model validation and parameter estimation for fractional-order and classical integer-order derivatives was carried out using real brucellosis for Egypt, 1999-2011. Overall, we noted that fractional-order model gave better prediction of brucellosis compared to classical integer-order model. Furthermore, we investigated the role of memory effects on the transmission of brucellosis in the population. We observe that, the memory effects have influenceon the transmission of brucellosis in the community. In addition, we noted that the aforementioned control strategies have the potential to reduce the transmission of brucellosis in the population. In particular, we observed that whenever the culling and vaccination rate is greater than 40% and 50% respectively, the disease dies out in the population.

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A Model for Brucellosis Disease Incorporating Age of Infection and Waning Immunity

Cited by 5 publications

References 33 publications

Dynamical Analysis of an Age-Structured SVEIR Model with Imperfect Vaccine

Dynamical Analysis of an Age-Structured SVEIR Model with Imperfect Vaccine

An Intrinsic Analysis of Human Brucellosis Dynamics in Africa

Dynamics and Analysis of Chronic Brucellosis in Sheep

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