Discipline: Mathematics and Statistics
Subcategory: Mathematics and Statistics
Room: Exhibit Hall A
Lanjing Bao - Georgia Gwinnett College, GA
Co-Author(s): Logan Rose, Marshall University, WV
Malaria is one of the most threatening public health concerns worldwide. While the governments and the non-profit organizations across the world have been fighting continuously against Malaria, the progress is not as significant as we expected. Statistically, WHO reports an estimation of 20 million cases reduction from 2010 to 2017; however, the number of cases of Malaria reported has increased comparing 2016 to 2017. Among the Malaria induced death globally, the children under five years old are the most vulnerable groups, and they account for 61% of the deaths. In effort to fight Malaria, a tremendous amount of funding is invested in controlling and elimination of Malaria. Insecticide-treated nets (ITN) are one of the most conventional and economic method; however, the limitation arises with the accessibility of ITN and the insecticide resistance developed in the Malaria vectors. Even though more than 50% of the susceptible population in endemic countries was protected by ITN by 2017, the coverage has come to saturation. Moreover, recent WHO report showed that resistance to the four commonly used insecticide classes pyrethroids, organochlorines, carbamates and organophosphates is widespread in all major malaria vectors across Malaria endemic countries. Among these, pyrethroids is the only insecticide class used to treat ITN, and vector resistance toward pyrethroids has been discovered in at least one type of Malaria vector over two third of these regions. We consider a malaria transmission model with SEIR (susceptible-exposed-infected-recovered) classes for the human population, SEI (susceptible-exposed-infected) classes for the wild mosquitoes and an additional class for sterile mosquitoes. We derive a formula for the basic reproduction number of infections. We formulate an optimal control problem in which the goal is to minimize both the infected human populations and the cost to implement two control strategies: the release of sterile mosquitoes (SIT) and the usage of insecticide-treated nets (ITN) to prevent the malaria transmission. Adjoint equations are derived and the characterization of the optimal controls are established. Finally, we quantify the effectiveness of the two interventions aimed at limiting the spread of Malaria. The basic reproduction number is calculated using Mathematica. Numerical simulations using Python and Matlab are provided to illustrate the results. We examined the basic reproduction number dependence on different mosquitoes release rates, and studied the Malaria transmission dynamics on various constant release rates. We simulated human and mosquitoes population dynamics using single control (either Sterile Mosquitoes Technique or Insecticide-Treated Nets (ITNs)), and a combination of two controls (Sterile Mosquitoes Technique and ITNs). We found the optimal control strategies under each circumference. It turns out the combination of both strategies leads to a more rapid elimination of the wild mosquito population that can suppress Malaria transmission.
Funder Acknowledgement(s): This study was supported by NSF REU #1757493 awarded at Middle Tennessee State University.
Faculty Advisor: Wandi Ding, firstname.lastname@example.org
Role: I contribute on equally half of all area in this research with Logan Rose from Marshall University in West Virginia. During the REU in the summer of 2019, we started the research on Malaria and the Mathematical model at the same time. From there, we continued to discuss and perform analysis which leads to the product of this research.