Understanding the Transmission Dynamics and Control of HIV Infection: A Mathematical Model Approach

Ajao, Saheed; Olopade, Isaac Adesola; Akinwumi, T. O.; Adewale, S. O.; Adesanya, Adegboyega Obatayo

doi:10.46481/jnsps.2023.1389

Cited by 5 publications

(2 citation statements)

References 21 publications

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“…The basic reproduction number generally given as R 0 is defined as the average number of new cases of an infection caused by one typical infectious individual, in a population consisting of susceptibles only [47][48][49]. According to Ref.…”

Section: The Basic Reproduction Numbermentioning

confidence: 99%

Modelling the co-infection of malaria and zika virus disease

Duru,

Mbah,

Anyanwu

et al. 2024

J. Nig. Soc. Phys. Sci.

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In this work, a new model for the co-infection of malaria and zika virus disease incorporating vaccination, treatment and vector control using sterile-insect technology (SIT) is formulated. The importance of this study is to highlight the possibility of the co-infection of humans with malaria and zika virus disease in any environment where both diseases co-circulate. Also, to suggest a new and comprehensive method for controlling the individual diseases and their co-infection. Through stability analysis, we showed that the disease-free equilibrium, (DFE) point of the co-infection model is locally asymptotically stable when the basic reproduction numbers, Rmz is less than one, and unstable otherwise. But, the DFE failed to be globally stable when Rmz < 1 which is an indication of existence of backward bifurcation in the model. This shows that bringing down the reproduction number, Rmz to less than one is not enough to eradicate the co-infection of the two diseases. Furthermore, it is shown that the two diseases have positive impact on the spread of each other, which could be attributed to misdiagnoses of one disease as the other. We also showed that effective treatment of infectious humans, increasing the rate of vaccination and employing sterile-insect technique to control the vectors significantly helped to control the individual diseases as well as the co-infection. From the results obtained in the study, it can be concluded that effective control of malaria and zika virus disease requires measures that will control their spread in both human and mosquito populations.

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Section: The Basic Reproduction Numbermentioning

confidence: 99%

Modelling the co-infection of malaria and zika virus disease

Duru,

Mbah,

Anyanwu

et al. 2024

J. Nig. Soc. Phys. Sci.

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“…In this paper, we propose a mathematical model for TB transmission dynamics featuring three infected classes: latent, active, and drug-resistant, incorporating optimal control strategies focusing on prevention and early treatment during the latent stage. Acknowledging the latent stage's critical importance in TB management, despite its lack of direct disease transmission, underscores the need for comprehensive approaches to address TB's complex dynamics and associated challenges [14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

A tuberculosis model with three infected classes

Sangotola,

Adeyemo,

Nuga

et al. 2024

J. Nig. Soc. Phys. Sci.

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The dynamics of tuberculosis within a population cannot be adequately represented by a single infectious class. Therefore, this study develops a compartmental model encompassing latent, active, and drug-resistant populations to better capture tuberculosis dynamics in a community. Model analysis reveals that the disease-free equilibrium point is locally asymptotically stable when the basic reproduction number is below one. Moreover, the use of a suitable Lyapunov function demonstrates global asymptotic stability of the disease-free equilibrium point. An endemic equilibrium emerges when the basic reproduction number exceeds one. Sensitivity analysis is conducted for each parameter associated with the basic reproduction number, and optimal control analysis is employed to assess the impact of various control strategies on disease containment. Numerical simulations are conducted to supplement theoretical findings, illustrating the practical implications of the proposed control strategies.

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