A Mathematical Measure to Fight Against Malaria and Exterminate Anopheles Mosquitoes

Atanyi Yusuf Emmanuel, Oduwole H.k and Utalor Kate Ifeoma
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Atanyi Yusuf Emmanuel: Department of Mathematics, Federal University of Lafia, PMB 146, Lafia, Nigeria
Oduwole H.k: Department of Mathematics, Nasarawa State University, Keffi,PMB 1022, Keffi, Nigeria
Utalor Kate Ifeoma: Mathematical Centre, Abuja, Nigeria

International Journal of Research and Innovation in Applied Science, 2023, vol. 8, issue 1, 115-200

Abstract: Modelling the effects of three natural predators on the aquatic and adult anopheles’ mosquitoes in the control of malaria transmission was aimed at eradicating anopheles’ larva, pupa and adult anopheles’ mosquito by introduction of natural predators “copepods, tadpoles and purple martins†(organism that eat up mosquito at larva, pupa, and adult stages), so that there should not be anopheles’ adult mosquito for malaria transmission in our society. This new proposed model is a control flow diagram of predator-prey interaction model in mosquito life-cycle that considers an open population of mosquito and predators. The population is sub-divided based on mosquito life-cycle and natural predators. Under a mosquito life-cycle, the population is divided into four compartments, Egg compartment E(t), Larva compartment L(t), Pupa compartment P(t), and Adult compartment A(t), and natural predators, it is divided into three compartments, namely; Copepods C_P (t), Tadpole〖 T〗_P (t) and Purple martins P_M (t). These models provide understanding for control of malaria in our environments, especially when the models are based on the ecology of the vector population and sound understanding of variables and parameters relevant for transmission. The model equations were derived using the model variables and parameters. The stability analysis of the free equilibrium states were analyzed using equilibrium point, elimination, substitution methods, idea of Beltrami’s and Diekmann’s conditions. From the stability analysis of steady state, we observed that the model free equilibrium state is stable, this implies that the equilibrium point or steady state is stable and the stability of the model(3.13.1) – (3.13.8) means, there will not be anopheles adult mosquito in our society for malaria transmission and from the idea of Beltrami’s and Diekmann’s conditions we observed that the Determinant of the Jacobian matrix is greater than zero(Det⠡〖{j}〗>0),Trace of the Jacobian matrix is less than zero(Tr{j}

Date: 2023
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