# New mathematical model of vertical transmission and cure of vector-borne diseases and its numerical simulation

New mathematical model of vertical transmission and cure of vector-borne diseases and its... In this research article, a new mathematical model for the transmission dynamics of vector-borne diseases with vertical transmission and cure is developed. The non-negative solutions of the model are shown. To understand the dynamical behavior of the epidemic model, the theory of basic reproduction number is used. As this number increases, the disease invades the population and vice versa. The effect of vertical transmission and cure rate on the basic reproduction number is shown. The disease-free and endemic equilibria of the model are found and both their local and global stabilities are presented. Finally, numerical simulations are carried out graphically to show the dynamical behaviors. These results show that vertical transmission and cure have a valuable effect on the transmission dynamics of the disease. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Difference Equations Springer Journals

# New mathematical model of vertical transmission and cure of vector-borne diseases and its numerical simulation

, Volume 2018 (1) – Feb 21, 2018
15 pages

/lp/springer_journal/new-mathematical-model-of-vertical-transmission-and-cure-of-vector-L0y67Zu9rY
Publisher
Springer International Publishing
Subject
Mathematics; Difference and Functional Equations; Mathematics, general; Analysis; Functional Analysis; Ordinary Differential Equations; Partial Differential Equations
eISSN
1687-1847
D.O.I.
10.1186/s13662-018-1516-z
Publisher site
See Article on Publisher Site

### Abstract

In this research article, a new mathematical model for the transmission dynamics of vector-borne diseases with vertical transmission and cure is developed. The non-negative solutions of the model are shown. To understand the dynamical behavior of the epidemic model, the theory of basic reproduction number is used. As this number increases, the disease invades the population and vice versa. The effect of vertical transmission and cure rate on the basic reproduction number is shown. The disease-free and endemic equilibria of the model are found and both their local and global stabilities are presented. Finally, numerical simulations are carried out graphically to show the dynamical behaviors. These results show that vertical transmission and cure have a valuable effect on the transmission dynamics of the disease.

### Journal

Published: Feb 21, 2018

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