Browsing by Author "Mpogolo, Godfrey Edward"

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    Mathematical modeling of the transmission dynamics of amoebiasis with some interventions
    (Europe PMC, 2022) Mwaijande, Stephen Edward; Mpogolo, Godfrey Edward
    A mathematical model for amoebiasis is developed and presented. The model captures some control interventions such as screening, treatment, and sanitation. The effective reproductive number is computed and is used to analyze the stability of the model system. Sensitivity analysis is used to investigate the parameters that impact the transmission of the disease; as such, it could need more attention to bring the disease to an end. Numerical results show a reduction in infections when at least each of the control measures considered is applied efficiently. Moreover, the findings show that carriers play a potential role in the prevalence of amoebiasis, ignoring them undermines the efforts of containing this epidemic. On the other hand, sensitivity analysis shows that indirect transmission contributes to more infections than direct transmission.
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    Modeling and optimal control of the transmission dynamics of amebiasis
    (Elsevier BV, 2023) Edward, Stephen; Mpogolo, Godfrey Edward
    In this paper, the mathematical models for amebiasis are developed and presented. The first model considers the transmission dynamics of amebiasis coupled with two constant controls: treatment and sanitation. The next-generation matrix calculates the effective reproductive number, which is then used to assess model system stability. A sensitivity analysis is performed to determine the primary factors affecting disease transmission. Nonetheless, the results suggest that indirect transmission is more crucial than direct transmission in spreading disease. In addition, we extended the first model to incorporate time-dependent optimal control measures, namely community awareness, treatment, and sanitation. The aim was to reduce the number of infections emanating from interaction with carriers, infected people, and polluted environments while minimizing the expenses associated with adopting controls. The optimal control problem is solved by applying Pontryagin’s Maximum Principle and forward and backward-in-time fourth-order Runge–Kutta methods. The results indicate that an awareness program is optimal when a single control strategy is the only available option. However, when a combination of two controls is implemented, an approach combining awareness programs and treatment is shown to be optimal. Generally, the best strategy is implementing a combination of all three controls: awareness programs, sanitation, and treatment.
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    Modeling and optimal control of the transmission dynamics of amebiasis
    (Elsevier BV, 2023) Edward, Stephen; Mpogolo, Godfrey Edward
    In this paper, the mathematical models for amebiasis are developed and presented. The first model considers the transmission dynamics of amebiasis coupled with two constant controls: treatment and sanitation. The next-generation matrix calculates the effective reproductive number, which is then used to assess model system stability. A sensitivity analysis is performed to determine the primary factors affecting disease transmission. Nonetheless, the results suggest that indirect transmission is more crucial than direct transmission in spreading disease. In addition, we extended the first model to incorporate time-dependent optimal control measures, namely community awareness, treatment, and sanitation. The aim was to reduce the number of infections emanating from interaction with carriers, infected people, and polluted environments while minimizing the expenses associated with adopting controls. The optimal control problem is solved by applying Pontryagin’s Maximum Principle and forward and backward-in-time fourth-order Runge–Kutta methods. The results indicate that an awareness program is optimal when a single control strategy is the only available option. However, when a combination of two controls is implemented, an approach combining awareness programs and treatment is shown to be optimal. Generally, the best strategy is implementing a combination of all three controls: awareness programs, sanitation, and treatment.