Transmission Dynamics of Zika Fever: A SEIR Based Model

In this paper, a deterministic model is proposed to perform a thorough investigation of the transmission dynamics of Zika fever. Our model, in particular, takes into account the effects of horizontal as well as vertical disease transmission of both humans and vectors. The expression for basic reprod...

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Bibliographic Details
Published in:Differential equations and dynamical systems 2021-07, Vol.29 (3), p.463-486
Main Authors: Imran, Mudassar, Usman, Muhammad, Dur-e-Ahmad, Muhammad, Khan, Adnan
Format: Article
Language:English
Subjects:
Asymptotic properties
Computer Science
Disease transmission
Engineering
Fever
Mathematics
Mathematics and Statistics
Original Research
Stability analysis
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Summary:In this paper, a deterministic model is proposed to perform a thorough investigation of the transmission dynamics of Zika fever. Our model, in particular, takes into account the effects of horizontal as well as vertical disease transmission of both humans and vectors. The expression for basic reproductive number R 0 is determined in terms of horizontal and vertical disease transmission rates. An in-depth stability analysis of the model is performed, and it is shown, that model is locally asymptotically stable when R 0 < 1 . In this case, there is a possibility of backward bifurcation in the model. With the assumption that total population is constant, we prove that the disease free state is globally asymptotically stable when R 0 < 1 . It is also shown that disease strongly uniformly persists when R 0 > 1 and there exists an endemic equilibrium which is unique if the total population is constant. The endemic state is locally asymptotically stable when R 0 > 1 .
ISSN:0971-3514
0974-6870
DOI:10.1007/s12591-017-0374-6