Global stability for a sheep brucellosis model with immigration

Sun, Gui‐Quan; Zhang, Zi-Ke

doi:10.1016/j.amc.2014.08.028

Cited by 52 publications

(27 citation statements)

References 32 publications

(42 reference statements)

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“…If only temporal (as opposed to spatial) dynamics is considered, the basic reproduction number-defined as "the average number of secondary cases caused by an infectious individual in a completely susceptible population" [11]-is the key quantity for determining the fate of epidemics. When this number is less than unity, a pathogen goes extinct regardless of the initial conditions; otherwise, the pathogen persists and the number of infections increases through time [11][12][13][14][15]. Although studies on the temporal dynamics of diseases proved insightful, observations that pathogens (like substances) diffuse from high to low density regions of space enticed the development of spatially explicit models capable of discerning, for example, disease transmission hotspots.…”

Section: Introductionmentioning

confidence: 99%

Pattern transitions in spatial epidemics: Mechanisms and emergent properties

Sun

Jusup

Jin

et al. 2016

Physics of Life Reviews

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219

115

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Infectious diseases are a threat to human health and a hindrance to societal development. Consequently, the spread of diseases in both time and space has been widely studied, revealing the different types of spatial patterns. Transitions between patterns are an emergent property in spatial epidemics that can serve as a potential trend indicator of disease spread. Despite the usefulness of such an indicator, attempts to systematize the topic of pattern transitions have been few and far between. We present a mini-review on pattern transitions in spatial epidemics, describing the types of transitions and their underlying mechanisms. We show that pattern transitions relate to the complexity of spatial epidemics by, for example, being accompanied with phenomena such as coherence resonance and cyclic evolution. The results presented herein provide valuable insights into disease prevention and control, and may even be applicable outside epidemiology, including other branches of medical science, ecology, quantitative finance, and elsewhere.

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Section: Introductionmentioning

confidence: 99%

Pattern transitions in spatial epidemics: Mechanisms and emergent properties

Sun

Jusup

Jin

et al. 2016

Physics of Life Reviews

Self Cite

219

115

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“…Sun and Zhang [7] discuss a sheep brucellosis model with immigration. From p.339 the corresponding characteristic equation is…”

Section: Lemma 2 the Condition Max{rmentioning

confidence: 99%

Proof of conjecture in: The basic reproduction number obtained from Jacobian and next generation matrices—A case study of dengue transmission modelling

Yang

Greenhalgh

2015

Applied Mathematics and Computation

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“…Some bacteria threshold can be seen in [12]. Also, there were many authors researching the brucellosis, who had been unconscious of the impact on immunization [13][14][15][16][17][18][19]. By referring to [20,21], we will put the pathogeny of brucellosis and MID into this paper.…”

Section: Introductionmentioning

confidence: 99%

Dynamical Analysis of the SEIB Model for Brucellosis Transmission to the Dairy Cows with Immunological Threshold

Zhang

et al. 2019

Complexity

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As we all know, bacteria is different from virus which with certain types can be killed by the immune cells in the body. The brucellosis, a bacterial disease, can invade the body by indirect transmission from environment, which has not been researched by combining with immune cells. Considering the effects of immune cells, we put a minimum infection dose of brucellosis invading into the dairy cows as an immunological threshold and get a switch model. In this paper, we accomplish a thorough dynamics analysis of a SEIB switch model. On the one hand, we can get a disease-free and bacteria-free steady state and up to three endemic steady states which may be thoroughly analyzed in different cases of a minimum infection dose in a switch model. On the other hand, we calculate the basic reproduction number R0 and know that the disease-free and bacteria-free steady state is a global stability when R0<1, and the one of the endemic steady state is a conditionally global stability when R0>1. We find that different amounts of R0 may lead to different steady states of brucellosis, and considering the effects of immunology is more serious in mathematics and biology.

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Global stability for a sheep brucellosis model with immigration

Cited by 52 publications

References 32 publications

Pattern transitions in spatial epidemics: Mechanisms and emergent properties

Pattern transitions in spatial epidemics: Mechanisms and emergent properties

Proof of conjecture in: The basic reproduction number obtained from Jacobian and next generation matrices—A case study of dengue transmission modelling

Dynamical Analysis of the SEIB Model for Brucellosis Transmission to the Dairy Cows with Immunological Threshold

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