Susceptible-infectious-susceptible (SIS) model with virus mutation in a variable population size

IF 3.1 3区 环境科学与生态学 Q2 ECOLOGY Ecological Complexity Pub Date : 2022-06-01 DOI:10.1016/j.ecocom.2022.101004
Ayse Peker Dobie
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引用次数: 5

Abstract

The complex dynamics of a contagious disease in which populations experience horizontal and vertical transmissions, size variation, and virus mutations are of considerable practical and theoretical interest. We model such a system by dividing a population into three distinct groups: susceptibles (S), C-infected (C) and F-infected (F), based on the Susceptible-Infectious-Susceptible (SIS) model. Once the individuals in the C-infected group recover from the disease, they gain no permanent immunity. The virus can mutate in the group C. When it does, the individuals become members of the F-infected group. The mutated virus causes a lethal and incurable disease with a high mortality rate. We discuss the model for two cases. For the first case, all the newborns from infected mothers develop the disease shortly after their birth. For the second case, there exist equal transmission rates and the C-infected population is lifelong infectious. Our analysis shows that both systems have positive solutions, and the first model possesses four equilibrium points, the trivial one (extinction of the species), C-free equilibrium (extinction of the ancestor virus) and two endemic equilibria of different properties. We identify the net population growth rates of the susceptible and C-infected groups for the existence of the equilibria of the first model. We define the conditions of parameters for which species extinction and endemic equilibria are locally asymptotically stable. We observe that bifurcation occurs at the C-free equilibrium. For the second model, we find that there is only one endemic equilibrium and it is always locally asymptotically stable. We also determine the region for the net population growth rates of the susceptible and F-infected groups for the existence of the endemic equilibrium.

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易感-感染-易感(SIS)模型在变种群大小的病毒突变
传染性疾病的复杂动力学,其中人群经历水平和垂直传播,大小变化和病毒突变,具有相当大的实践和理论意义。我们基于易感-感染-易感(SIS)模型,通过将人群分为三个不同的群体:易感人群(S)、C型感染人群(C)和F型感染人群(F)来建立这样一个系统的模型。一旦c型感染组的个体从疾病中恢复过来,他们就不会获得永久的免疫力。病毒可以在c组中发生变异,当它发生变异时,这些个体就成为f感染组的成员。这种变异的病毒会导致一种致命的、无法治愈的疾病,死亡率很高。我们讨论两种情况下的模型。对于第一个病例,所有受感染母亲所生的新生儿在出生后不久就会患上该病。对于第二种情况,存在相同的传播率,c感染人群具有终身传染性。我们的分析表明,这两个系统都有正解,并且第一个模型具有四个平衡点,一个平凡平衡点(物种灭绝),一个无c平衡点(祖先病毒灭绝)和两个不同性质的地方性平衡点。我们确定了存在第一个模型平衡点的易感和c感染群体的净人口增长率。我们定义了物种灭绝和地方性平衡是局部渐近稳定的参数条件。我们观察到分岔发生在无碳平衡态。对于第二个模型,我们发现只有一个局部平衡点,它总是局部渐近稳定的。我们还确定了存在地方性平衡的易感和f感染群体的净人口增长率区域。
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来源期刊
Ecological Complexity
Ecological Complexity 环境科学-生态学
CiteScore
7.10
自引率
0.00%
发文量
24
审稿时长
3 months
期刊介绍: Ecological Complexity is an international journal devoted to the publication of high quality, peer-reviewed articles on all aspects of biocomplexity in the environment, theoretical ecology, and special issues on topics of current interest. The scope of the journal is wide and interdisciplinary with an integrated and quantitative approach. The journal particularly encourages submission of papers that integrate natural and social processes at appropriately broad spatio-temporal scales. Ecological Complexity will publish research into the following areas: • All aspects of biocomplexity in the environment and theoretical ecology • Ecosystems and biospheres as complex adaptive systems • Self-organization of spatially extended ecosystems • Emergent properties and structures of complex ecosystems • Ecological pattern formation in space and time • The role of biophysical constraints and evolutionary attractors on species assemblages • Ecological scaling (scale invariance, scale covariance and across scale dynamics), allometry, and hierarchy theory • Ecological topology and networks • Studies towards an ecology of complex systems • Complex systems approaches for the study of dynamic human-environment interactions • Using knowledge of nonlinear phenomena to better guide policy development for adaptation strategies and mitigation to environmental change • New tools and methods for studying ecological complexity
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