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.
Highlights
1 Introduction Vector-borne diseases are infectious diseases transmitted to humans and animals by blood-feeding arthropods
Some common vector-borne diseases are West Nile virus, dengue fever, Rift Valley fever, malaria, and viral encephalitis caused by pathogens such as bacteria, viruses, and parasites
In case of some diseases such as AIDS and Hepatitis B, it is possible for the offspring of infected parents to be born infected
Summary
Vector-borne diseases are infectious diseases transmitted to humans and animals by blood-feeding arthropods. Vector-borne infectious diseases remain amongst the Abdullah et al Advances in Difference Equations (2018) 2018:66 most important cause of global health illness and are major killers, of children. Our paper involves such an epidemic model for the transmission dynamics of vector-borne diseases that incorporates both horizontal and vertical transmission in the vector–host population.
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