scholarly journals A Fractional-Order Model for Zika Virus Infection with Multiple Delays

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-20 ◽  
Author(s):  
R. Rakkiyappan ◽  
V. Preethi Latha ◽  
Fathalla A. Rihan
Keyword(s):  
Hopf Bifurcation ◽  
Virus Infection ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Zika Virus ◽  
Epidemic Model ◽  
Time Delays ◽  
Multiple Delays ◽  
Multiple Time ◽  
Zika Virus Infection

Time delays and fractional order play a vital role in biological systems with memory. In this paper, we propose an epidemic model for Zika virus infection using delay differential equations with fractional order. Multiple time delays are incorporated in the model to consider the latency of the infection in a vector and the latency of the infection in the infected host. We investigate the necessary and sufficient conditions for stability of the steady states and Hopf bifurcation with respect to three time delays τ1, τ2, and τ3. The model undergoes a Hopf bifurcation at the threshold parameters τ1∗, τ2∗, and τ3∗. Some numerical simulations are given to show the effectiveness of obtained results. The numerical simulations confirm that combination of fractional order and time delays in the epidemic model effectively enriches the dynamics and strengthens the stability condition of the model.

Stability and Hopf Bifurcation Analysis in Hindmarsh–Rose Neuron Model with Multiple Time Delays

2016 ◽  
Vol 26 (11) ◽  
pp. 1650187 ◽  
Author(s):  
Dongpo Hu ◽  
Hongjun Cao
Keyword(s):  
Hopf Bifurcation ◽  
Numerical Simulations ◽  
Time Delays ◽  
Single Neuron ◽  
Neuron Model ◽  
Multiple Time ◽  
Bifurcation Diagrams ◽  
Dynamical Behaviors ◽  
Multiple Time Delays ◽  
The Stability

In this paper, the dynamical behaviors of a single Hindmarsh–Rose neuron model with multiple time delays are investigated. By linearizing the system at equilibria and analyzing the associated characteristic equation, the conditions for local stability and the existence of local Hopf bifurcation are obtained. To discuss the properties of Hopf bifurcation, we derive explicit formulas to determine the direction of Hopf bifurcation and the stability of bifurcated periodic solutions occurring through Hopf bifurcation. The qualitative analyses have demonstrated that the values of multiple time delays can affect the stability of equilibrium and play an important role in determining the properties of Hopf bifurcation. Some numerical simulations are given for confirming the qualitative results. Numerical simulations on the effect of delays show that the delays have different scales when the two delay values are not equal. The physiological basis is most likely that Hindmarsh–Rose neuron model has two different time scales. Finally, the bifurcation diagrams of inter-spike intervals of the single Hindmarsh–Rose neuron model are presented. These bifurcation diagrams show the existence of complex bifurcation structures and further indicate that the multiple time delays are very important parameters in determining the dynamical behaviors of the single neuron. Therefore, these results in this paper could be helpful for further understanding the role of multiple time delays in the information transmission and processing of a single neuron.

scholarly journals Stability and Hopf Bifurcation Analysis of a Fractional-Order Epidemic Model with Time Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Zhen Wang ◽  
Xinhe Wang
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Numerical Simulations ◽  
Equilibrium Point ◽  
Fractional Order ◽  
Bifurcation Analysis ◽  
Epidemic Model ◽  
Bifurcation Parameter ◽  
Theoretical Results ◽  
Disease Free

A fractional-order epidemic model with time delay is considered. Firstly, stability of the disease-free equilibrium point and endemic equilibrium point is studied. Then, by choosing the time delay as a bifurcation parameter, the existence of Hopf bifurcation is studied. Finally, numerical simulations are given to illustrate the effectiveness and feasibility of theoretical results.

Congenital Zika Virus Infection Paradigm: What is in the Wardrobe? A Narrative Review

2019 ◽  
Vol 1 (1) ◽  
pp. 49-56
Author(s):  
Mariam M. Mirambo ◽  
Lucas Matemba ◽  
Mtebe Majigo ◽  
Stephen E. Mshana
Keyword(s):  
Virus Infection ◽  
Neural Tube ◽  
Zika Virus ◽  
English Language ◽  
Case Reports ◽  
Case Series ◽  
Epidemiological Studies ◽  
Ocular Manifestations ◽  
Zika Virus Infection ◽  
N 93

Background: Zika virus infection during pregnancy has been recently associated with congenital microcephaly and other severe neural tube defects. However, the magnitude of confirmed cases and the scope of these anomalies have not been extensively documented. This review focuses on the magnitude of laboratory-confirmed congenital Zika virus cases among probable cases and describing the patterns of congenital anomalies allegedly caused by the Zika virus, information which will inform further research in this area. Methods: We conducted a literature search for English-language articles about congenital Zika virus infection using online electronic databases (PubMed/MEDLINE, POPLINE, Embase, Google Scholar, and Web of Knowledge). The search terms used were, “zika”, “pregnancy”, [year], “microcephaly”, “infants”, “children”, “neonates”, “foetuses”, “neural tube defect”, and “CNS manifestations” in different combinations. All articles reporting cases or case series between January 2015 and December 2016 were included. Data were entered into a Microsoft Excel database and analysed to obtain proportions of the confirmed cases and patterns of anomalies. Results: A total of 24 articles (11 case series, 9 case reports, and 4 others) were found to be eligible and included in this review. These articles reported 919 cases, with or without microcephaly, presumed to have congenital Zika virus infection. Of these cases, 884 (96.2%) had microcephaly. Of the 884 cases of microcephaly, 783 (88.6%) were tested for Zika virus infection, and 216 (27.6%; 95% confidence interval, 24.5% to 30.8%) were confirmed to be Zika virus-positive. In addition to microcephaly, other common abnormalities reported – out of 442 cases investigated – were calcifications of brain tissue (n=240, 54.3%), ventriculomegaly (n=93, 20.8%), cerebellar hypoplasia (n=52, 11.7%), and ocular manifestations (n=46, 10.4%). Conclusion: Based on the available literature, Zika virus infection during pregnancy might lead to a wide array of outcomes other than microcephaly. There is a need for more epidemiological studies in Zika-endemic areas, particularly in Africa, to ascertain the role of Zika virus in causing congenital neurological defects.

Congenital Zika Virus Infection Paradigm: What is in the Wardrobe? A Narrative Review

2019 ◽  
Vol 1 (1) ◽  
pp. 49-56
Author(s):  
Mariam M. Mirambo ◽  
Lucas Matemba ◽  
Mtebe Majigo ◽  
Stephen E. Mshana
Keyword(s):  
Virus Infection ◽  
Neural Tube ◽  
Zika Virus ◽  
English Language ◽  
Case Reports ◽  
Case Series ◽  
Epidemiological Studies ◽  
Ocular Manifestations ◽  
Zika Virus Infection ◽  
N 93

Background: Zika virus infection during pregnancy has been recently associated with congenital microcephaly and other severe neural tube defects. However, the magnitude of confirmed cases and the scope of these anomalies have not been extensively documented. This review focuses on the magnitude of laboratory-confirmed congenital Zika virus cases among probable cases and describing the patterns of congenital anomalies allegedly caused by the Zika virus, information which will inform further research in this area. Methods: We conducted a literature search for English-language articles about congenital Zika virus infection using online electronic databases (PubMed/MEDLINE, POPLINE, Embase, Google Scholar, and Web of Knowledge). The search terms used were, “zika”, “pregnancy”, [year], “microcephaly”, “infants”, “children”, “neonates”, “foetuses”, “neural tube defect”, and “CNS manifestations” in different combinations. All articles reporting cases or case series between January 2015 and December 2016 were included. Data were entered into a Microsoft Excel database and analysed to obtain proportions of the confirmed cases and patterns of anomalies. Results: A total of 24 articles (11 case series, 9 case reports, and 4 others) were found to be eligible and included in this review. These articles reported 919 cases, with or without microcephaly, presumed to have congenital Zika virus infection. Of these cases, 884 (96.2%) had microcephaly. Of the 884 cases of microcephaly, 783 (88.6%) were tested for Zika virus infection, and 216 (27.6%; 95% confidence interval, 24.5% to 30.8%) were confirmed to be Zika virus-positive. In addition to microcephaly, other common abnormalities reported – out of 442 cases investigated – were calcifications of brain tissue (n=240, 54.3%), ventriculomegaly (n=93, 20.8%), cerebellar hypoplasia (n=52, 11.7%), and ocular manifestations (n=46, 10.4%). Conclusion: Based on the available literature, Zika virus infection during pregnancy might lead to a wide array of outcomes other than microcephaly. There is a need for more epidemiological studies in Zika-endemic areas, particularly in Africa, to ascertain the role of Zika virus in causing congenital neurological defects.

Spatial distribution of Zika virus infection in northeastern Colombia

2016 ◽  
Author(s):  
Alfonso J Rodriguez-Morales ◽  
Ubydul Haque ◽  
Jacob D Ball ◽  
Carlos Julian García-Loaiza ◽  
Maria Leonor Galindo-Marquez ◽  
...  
Keyword(s):  
Spatial Distribution ◽  
Virus Infection ◽  
Zika Virus ◽  
Zika Virus Infection
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