Browsing by Author "Dejen Agachew"

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    Mathematical Modelling of Malaria Transmission Dynamics with Optimal Control Strategies
    (Addis Ababa University, 2024-08) Dejen Agachew; Manalebish Debalke
    Malaria is a tropical disease caused primarily by Plasmodium falciparum, which has been humanity’s major adversary to this day. This research proposes a malaria model that incorporates the use of treated mosquito nets as a disease control approach, which is then turned into proportions to estimate the worldwide impact of ITNs on malaria prevalence. Using a matrixtheoretic approach to construct a Lyapunov function results in a malaria-free equilibrium state that is globally asymptotically stable if the control reproduction number,Rm < 1. This suggests that malaria can be controlled or eradicated beneath a certain threshold amount,Rm. A malaria-persistence equilibrium state occurs and is globally stable for Rm > 1, utilizing the geometric theoretic technique with the Lozoskii measure. Numerical experiments show that the prevalence of infection can be reduced to zero if the fraction of vulnerable persons using treated mosquito nets exceeds a particular threshold number.