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All Journal Asian Journal of Science, Technology, Engineering, and Art Mikailalsys Journal of Mathematics and Statistics
M, Bulus S.
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Arts Computer Science & IT Engineering Mathematics Mechanical Engineering Social Sciences

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A Mathematical Model for Malaria Disease Dynamics with Relapse Parameter K, Adamu A.; B, Williams; M, Bulus S.
Mikailalsys Journal of Mathematics and Statistics Vol 3 No 1 (2025): Mikailalsys Journal of Mathematics and Statistics
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjms.v3i1.4985

Abstract

Malaria is one of the oldest diseases that has been extensively researched from multiple perspectives. Although many infectious diseases, including malaria, are preventable, they remain widespread in numerous communities due to insufficient, delayed, or ineffective control measures. Effective disease control involves rapidly reducing the infected population when a cure is available and minimizing susceptibility through vaccination when possible. Since malaria vaccines are still under development, vaccination offers a potential strategy for reducing the number of susceptible individuals. In this paper, we have analyzed and modified the SPITR mathematical model by Adamu et al. (2017) to study the transmission and control of malaria. Our modifications include the incorporation of a relapse parameter, and we have determined the basic reproduction number for the revised model. We demonstrated that the disease-free equilibrium (DFE) is locally asymptotically stable when the reproduction number is less than one and becomes unstable when it exceeds one. This finding suggests that with a combination of effective treatment, malaria relapse rate can be reduced and malaria in general can be effectively controlled in the population if the reproduction number is kept below unity.
On Models of Malaria with Natural Recovery K, Adamu A.; M, Bulus S.; B, Williams; D, Yavalah
Asian Journal of Science, Technology, Engineering, and Art Vol 3 No 2 (2025): Asian Journal of Science, Technology, Engineering, and Art
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/ajstea.v3i2.5020

Abstract

This study presents a mathematical model for malaria transmission dynamics, incorporating natural recovery and public awareness/sensitization within the human population. The model evaluates the impact of sensitization alongside conventional control strategies in mitigating malaria spread. Through qualitative analysis, the basic reproduction number was determined to be less than unity, suggesting the feasibility of disease control. Additionally, stability analysis confirmed that the disease-free equilibrium is locally and asymptotically stable. Our findings indicate that, with a combination of natural recovery, public sensitization, and conventional interventions, malaria can be successfully eradicated from the population.
Modeling the Impact of Vector Reduction and Natural Recovery on the Transmission Dynamics of Malaria K, Adamu A.; O, Ajor E.; A, Olopade I.; M, Bulus S.; W, Barde; D, Yavalah
Asian Journal of Science, Technology, Engineering, and Art Vol 3 No 3 (2025): Asian Journal of Science, Technology, Engineering, and Art
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/ajstea.v3i3.5396

Abstract

A mathematical modeling of the impact of vector reduction and natural recovery on the transmission dynamics of malaria was carried out. We present a deterministic model for the transmission dynamics of malaria in which natural recovery and vector reduction were both important for the disease management. We estimated the basic reproduction number using the next generation matrix method and investigated the local stability of the disease free equilibrium points of the model. Sensitivity analysis and Numerical simulations of the basic reproduction number with respect to the model parameters were carried out. Our result shows that effective vector reduction and increased natural recovery will reduce the spread of malaria.
Co-Authors A, Olopade I. B, Williams D, Yavalah K, Adamu A. O, Ajor E. W, Barde