Research Article
Ecoepidemiological Model and Analysis of MSV Disease
Transmission Dynamics in Maize Plant
Haileyesus Tessema Alemneh ,
1
Oluwole Daniel Makinde ,
2
and David Mwangi Theuri
3
1
Pan African University Institute of Basic Sciences, Technology and Innovation, Nairobi, Kenya
2
Faculty of Military Science, Stellenbosch University, Stellenbosch, South Africa
3
Department of Mathematics, Jomo Kenyatta University, Nairobi, Kenya
Correspondence should be addressed to Haileyesus Tessema Alemneh; haila.tessema@gmail.com
Received 1 September 2018; Revised 12 November 2018; Accepted 20 December 2018; Published 20 January 2019
Academic Editor: Harvinder S. Sidhu
Copyright © 2019 Haileyesus Tessema Alemneh et al. Tis is an open access article distributed under the Creative Commons
Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is
properly cited.
In this paper, an ecoepidemiological deterministic model for the transmission dynamics of maize streak virus (MSV) disease in
maize plant is proposed and analysed qualitatively using the stability theory of diferential equations.Te basic reproduction number
with respect to the MSV free equilibrium is obtained using next generation matrix approach. Te conditions for local and global
asymptotic stability of MSV free and endemic equilibria are established. Te model exhibits forward bifurcation and the sensitivity
indices of various embedded parameters with respect to the MSV eradication or spreading are determined. Numerical simulation
is performed and dispalyed graphically to justify the analytical results.
1. Introduction
Maize (Zea mays L.) is grown globally across temperate and
tropical zones, spanning all continents [1]. It is the most
widely grown and consumed staple crop in Africa with more
than 100 million Africans depending on it as their main
food source which is annually planted over an area of 15.5
million hectares [2, 3]. In Ethiopia, maize is the most cereal
gown which ranks frst in yield per hectare and is grown
in all 11 administrative regions [4]. It is the primary food,
averaging slightly more than 20% of daily caloric intake.
About 9 million smallholder farmers grow maize and 75% of
the maize produced is consumed as food [5, 6]. Te reports
of Ethiopian Commodity Exchange show that three-fourth
of maize produced is used for household expenditure; only
about ten percent is marketed and the remaining is used for
seed, in-kind expenses for labor and animal feed [6].
Maize production is constrained by many abiotic and
biotic factors of which maize streak disease (MSD) is the
major biotic threat in Ethiopia. It is the most destructive and
devastating disease of maize in Sub-Saharan Africa which
is caused by maize streak virus (MSV; genus Mastrevirus,
family Geminiviridae) [3, 7] including Ethiopia [4]. MSV is
a major constraint to maize and over 80 other crops species
[8] including oats, wheat, sorghum, millet, fnger millet, and
sugarcane [2, 9]. MSD is a major threat to cereal crops
amongst smallholder farmers in Sub-Saharan Africa causing
up to US $ 480 million losses annually [10]. MSD is a viral
disease which has single-component, circular, ssDNA [2, 3].
MSV has been reported to be the most economically sig-
nifcant causing 100% yield loss if infection occurs in the frst
three weeks of planting maize [3, 11]. It is irregular in nature
and transmitted in a persistent manner by leafoppers in the
genus Cicadulina [2, 5]. Globally, 22 species of Cicadulina
leafoppers have been reported, of which 18 are found in
Africa. Cicadulina mbila is the most predominant vector and
the most important in the epidemiology of the virus [2] from
the 8 known vectors of MSV in the genus. In Ethiopia, fve of
these 22 known species of Cicadulina have been recorded [4].
Mathematical modeling is an important tool used in
analyzing the dynamics of infectious diseases. Several models
have been formulated and analyzed to explain the dynamics
of plant disease transmission. Te authors in [12] investigated
the impacts of foliar diseases on maize plant population
Hindawi
International Journal of Mathematics and Mathematical Sciences
Volume 2019, Article ID 7965232, 14 pages
https://doi.org/10.1155/2019/7965232