Research Article Global Stability of Malaria Transmission Dynamics Model with Logistic Growth Abadi Abay Gebremeskel Department of Mathematics, Haramaya University, Haramaya, Ethiopia Correspondence should be addressed to Abadi Abay Gebremeskel; abaybeti@yahoo.com Received 6 December 2017; Revised 5 February 2018; Accepted 25 February 2018; Published 29 March 2018 Academic Editor: Zhengqiu Zhang Copyright © 2018 Abadi Abay Gebremeskel. 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. Mathematical models become an important and popular tools to understand the dynamics of the disease and give an insight to reduce the impact of malaria burden within the community. Tus, this paper aims to apply a mathematical model to study global stability of malaria transmission dynamics model with logistic growth. Analysis of the model applies scaling and sensitivity analysis and sensitivity analysis of the model applied to understand the important parameters in transmission and prevalence of malaria disease. We derive the equilibrium points of the model and investigated their stabilities. Te results of our analysis have shown that if  0 ≤1, then the disease-free equilibrium is globally asymptotically stable, and the disease dies out; if  0 >1, then the unique endemic equilibrium point is globally asymptotically stable and the disease persists within the population. Furthermore, numerical simulations in the application of the model showed the abrupt and periodic variations. 1. Introduction Malaria is a mosquito-borne disease caused by Plasmodium parasite, which is transmitted through the bites of an infected mosquito. In 2017, the World Health Organization report reveals estimations of 216 million malaria cases and 445 thousand deaths due to malaria were registered worldwide in 2016. However, the most malaria cases and deaths were shared by the WHO Africa region, which account for 90% of cases and 91% deaths. Te most predominant malaria parasite in the WHO Africa region is Plasmodium falciparum, accounting for 99% of malaria cases in 2016 [1]. Malaria is entirely preventable and treatable disease if the recommended interventions are properly applied. Indi- viduals should have taken some aggressive measurements to decline malaria burden. Personal protection measures are the frst line of defense against mosquito-borne diseases. Mosquito repellent is a method used for personal protection; and these are the substances used for exposed skin to prevent human-mosquito contact. Insecticide Treated Bed Nets (ITNs) are used for individuals against malaria to reduce the morbidity of childhood malaria (below fve years of age) by 50% and global child mortality by 20–30% [2, 3]. When used on a large scale, ITNs are supposed to represent efcient tools for malaria vector control but there is a limitation of resistance to insecticides used for a saturated net. Te resistance of the most important African malaria Anopheles gambiae to protrude is already widespread in several West African countries [4, 5]. Nowadays, mathematical models become an important and popular tools to understand the transmission dynamics of the disease and give an insight to reduce the impact of malaria burden in the society. Tis is because mathematical modeling can answer the following questions raised by the public health authorities and policy makers to make the correct decisions: (1) how severe will the epidemics be? (2) How long will it last? (3) How efective will an intervention be? (4) What are the efective measures to control and eliminate an endemic disease? Te earliest malaria model study originated from Ross in 1911 [6] and later modifcation made by Macdonald [7]. Some further extensions of Ross- Macdonald models for malaria were described in [8–13]. Tumwiine et al. [13] defne the reproduction number,  0 , and show the existence and stability of the disease-free equilibrium and an endemic equilibrium. Hindawi Discrete Dynamics in Nature and Society Volume 2018, Article ID 5759834, 12 pages https://doi.org/10.1155/2018/5759834