Research Article
Impact of Awareness to Control Malaria Disease: A Mathematical
Modeling Approach
Malik Muhammad Ibrahim ,
1
Muhammad Ahmad Kamran ,
2
Malik Muhammad Naeem Mannan ,
3
Sangil Kim ,
1
and Il Hyo Jung
1,4
1
Department of Mathematics, Pusan National University, Busan 46241, Republic of Korea
2
Department of Cogno-Mechatronics, Pusan National University, Busan 46241, Republic of Korea
3
School of Allied Health Sciences, Griffith University, Gold Coast, Australia
4
Finance Fishery Manufacture Industrial Mathematics Center on Big Data, Pusan National University,
Busan 46241, Republic of Korea
Correspondence should be addressed to Sangil Kim; sangil.kim@pusan.ac.kr and Il Hyo Jung; ilhjung@pusan.ac.kr
Received 29 April 2020; Revised 30 July 2020; Accepted 10 August 2020; Published 28 October 2020
Academic Editor: Tongqian Zhang
Copyright © 2020 Malik Muhammad Ibrahim et al. is 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.
e mathematical modeling of malaria disease has a crucial role in understanding the insights of the transmission dynamics and
corresponding appropriate prevention strategies. In this study, a novel nonlinear mathematical model for malaria disease has been
proposed. To prevent the disease, we divided the infected population into two groups, unaware and aware infected individuals. e
growth rate of awareness programs impacting the population is assumed to be proportional to the unaware infected individuals. It
is further assumed that, due to the effect of awareness campaign, the aware infected individuals avoid contact with mosquitoes. e
positivity and the boundedness of solutions have been derived through the completing differential process. Local and global
stability analysis of disease-free equilibrium has been investigated via basic reproductive number R
0
,if R
0
< 1, the system is stable
otherwise unstable. e existence of the unique endemic equilibrium has been also determined under certain conditions. e
solution to the proposed model is derived through an iterative numerical technique, the Runge–Kutta method. e proposed
model is simulated for different numeric values of the population of humans and anopheles in each class. e results show that a
significant increase in the population of susceptible humans is achieved in addition to the decrease in the population of the
infected mosquitoes.
1. Introduction
Malaria is an ancient disease with challenging health issues.
e tropical regions such as Africa, Asia, and America are
favorable for the rapid spread of this disease [1]. In 2018,
there are estimated two-hundred and twenty-eight million
cases of malaria around the world. is deadly disease is the
root cause of the death of four-hundred-five thousand
people according to the World Health Organization (WHO)
2019 world malaria report [2]. is disease is originated by
the plasmodium parasite. e transmission of this infection
to human body is by the bite of a female mosquito. Medical
symptoms such as a rise in the body temperature, fatigue,
pain, shivering, and sweats may occur within a few days after
an infected mosquito bite. Till the time, there is no effective
vaccine developed and some existing antimalarial drugs are
losing their effectiveness due to the drug resistance evolved
in the parasite [3].
e literature on the mathematical model for vector-
borne disease likewise malaria is vast. e first published
model demonstrating the life cycle of the malaria parasite
was developed by Sir Ross [4]. e model proposed by Sir
Ronald Ross is one of the simplest models, known as the
classical Ross model in the literature. It demonstrates the
crosstalk between the number of mosquitoes and the pro-
portion of bite that produced infection in the human body.
Hindawi
Complexity
Volume 2020, Article ID 8657410, 13 pages
https://doi.org/10.1155/2020/8657410