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■Bio-mathematics, Statistics and Nano-Technologies: Mosquito Control Strategies

to different diseases, e.g., Malaria [12, 32, 51], and Zika [14, 31] and Dengue [41, 43]

viruses, which are infections transmitted primarily by Aedes mosquitos.

Optimal control theory is an area of mathematical optimization that deals with finding a

control for a dynamical system over a period of time such that an objective function is opti-

mized [10, 34]. While classical applications are essentially found in engineering, physics,

economy and business [19, 23, 29, 50], more recent applications are found in medicine,

infectious diseases and epidemiology [15, 21, 26, 28]. For example, optimal control has

shown to be very useful with respect to human respiratory infections [42], cholera [20, 21],

tuberculosis [44], HIV [5, 37, 38], Ebola [8, 36], malaria [33, 45], Zika [6, 48], and dengue

epidemics [39, 40]. Here we focus on optimal control to Malaria prevention via insecticide-

treated nets [45].

Malaria is a life threatening disease caused by Plasmodium parasites and transmitted

from one individual to another by the bite of infected female anopheline mosquitos [3, 51].

In the human body, the parasites multiply in the liver, and then infect red blood cells. Fol-

lowing World Health Organization (WHO) 2019 report, an estimated 228 million cases of

malaria occurred worldwide (95% confidence interval [CI]: 206–258 million), with most

malaria cases from WHO African Region (213 million or 93%), followed by the WHO

South-East Asia Region with 3.4% of the cases and the WHO Eastern Mediterranean Re-

gion with 2.1% [55]. Malaria is an entirely preventable and treatable disease, provided the

currently recommended interventions are properly implemented. Following WHO, these

interventions include (i) vector control through the use of insecticide-treated nets (ITNs),

indoor residual spraying and, in some specific settings, larval control, (ii) chemopreven-

tion for the most vulnerable populations, particularly pregnant women and infants, (iii)

confirmation of malaria diagnosis through microscopy or rapid diagnostic tests for every

suspected case, and (iv) timely treatment with appropriate antimalarial medicines [55].

An ITN is a mosquito net that repels, disables and/or kills mosquitos coming into contact

with insecticide on the netting material. ITNs are considered one of the most effective in-

terventions against malaria [22]. In 2007, WHO recommended full ITN coverage of all

people at risk of malaria, even in high-transmission settings [54]. By 2011, 32 countries in

the African region and 78 other countries worldwide, had adopted the WHO recommen-

dation. A total of 89 countries, including 39 in Africa, distribute ITNs free of charge. Be-

tween 2004 and 2010, the number of ITNs delivered annually by manufacturers to malaria-

endemic countries in sub-Saharan Africa increased from 6 million to 145 million. Between

2016 and 2018, a total of 578 million ITNs were reported by manufacturers as having

been delivered globally, with 50% going to Côte d’Ivoire, the Democratic Republic of the

Congo, Ethiopia, Ghana, India, Nigeria, Uganda and the United Republic of Tanzania. In

2018, about 197 million ITNs were delivered by manufacturers, of which more than 87%

were delivered to countries in sub-Saharan Africa. Globally, 80% of ITNs were distributed

through mass distribution campaigns, 10% in antenatal care facilities and 6% as part of

immunization programmes [55]. However, there is still an urgent need to identify new

funding sources to maintain and expand coverage levels of interventions so that outbreaks

of disease can be avoided and international targets for reducing malaria cases and deaths

can be attained.