Introduction and Overview

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Theory. Interventions usually include vector control through insecticide-treated nets (ITNs)

and Human behavior change interventions, including information, education, and commu-

nication (IEC) campaigns. Mathematical models can be introduced mimicking ITN and

IEC interventions using Optimal Control Theory. Resulting equations can be solved to

minimize the number of infectious humans while keeping costs low. At the end of the

chapter, numerical results are provided, showing the effectiveness of the optimal control

interventions. In the final chapter of this section or part, a deterministic model based on

SIRUV is used and analyzed by complexity reduction using time scale separation and sin-

gular perturbation analysis. This method allows the representation of host-only models

connected to vector-borne disease dynamics without including the mosquito population.

The fourth section is dedicated to topological concepts applied to mosquito control.

This field is relatively unexplored. For instance, developing a solid theory connecting the

topological characteristics of an area under mosquito control with mathematical models us-

ing Optimal Control Theory needs to be better understood mathematically and developed.

Many considerations must be taken into account when designing the regions for spraying,

fogging, or ground placement of insecticides. These include the type of mosquito being

eradicated, their flight ranges, flight patterns of vectors, population density, and already

used control measures in the region. Also of concern is the region’s demographics to be

sprayed, including vulnerable populations and its topography. Political issues must often

be considered, e.g., public opposition to spraying, which is very similar to the matters of

interest when designing voting districts, which is the mathematical expertise of the author.

The fifth section aims to design and model efficient mosquito repellents. Most re-

pellents, insecticides, and pesticides contain biological and natural chemical compounds.

Discoveries and developments in novel biologically active compounds are largely poten-

tiated by computational and numerical methods using tools like chemometrics, mathe-

matical modeling, and molecular docking. Since mosquitos rapidly develop resistance to

repelling compounds, it is necessary to involve various chemometric techniques to shorten

the time for laboratory experiments and save resources in searching for new effective re-

pellents. Multiple linear regression (MLR), principal component regression (PCR), partial

least squares (PLS), and artificial neural networks (ANN), together with pattern recognition

techniques such as principal component analysis (PCA) and hierarchical cluster analysis

(HCA), as well as molecular docking approach, can be used for screening of many com-

pounds with potential repelling or different physicochemical properties. Ideas about the

development of effective vaccines are also briefly discussed.

The sixth section is focused on the pharmacological treatment of malaria with the

quick and complete removal of the Plasmodium parasites from a patient’s circulation to

prevent uncomplicated malaria from progressing to a severe infection or mortality. It is

well known that effective malaria management also decreases disease transmission to other

population members by decreasing the disease reservoir and preventing the emergence and

spread of resistance to antimalarial drugs.