Optimal control of intervention strategies in malaria–tuberculosis co-infection with relapse

Mwamtobe, Peter Mpasho; Simelane, Simphiwe; Abelman, Shirley; Tchuenche, Jean M.

doi:10.1142/s1793524518500171

Cited by 9 publications

(8 citation statements)

References 20 publications

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“…Castillo-Chavez and Song [15] provided a comprehensive review of the dynamics and control of tuberculosis. Standard disease transmission and control models in which the majority of the population steadily grows over time are presented in [16,17]. Establishing the stability properties of a dynamic system is a difficult problem in general.…”

Section: Introductionmentioning

confidence: 99%

“…Korobeinikov [18,19] presented a family of Lyapunov functions for three-compartment epidemiological models that appear to be useful for more complex models. Furthermore, mathematical models have been used to understand the dynamic transmission of diseases such as malaria [17,20], hepatitis [21], tuberculosis [22], dengue [23], and COVID-19 [24], and to understand the underlying dynamics of the target-mediated drug disposition [25][26][27]. Co-infections by multiple pathogens are common and theory predicts co-infections to have major consequences for both within-and between-host disease dynamics [17,28].…”

Section: Introductionmentioning

confidence: 99%

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Modeling visceral leishmaniasis and tuberculosis co-infection dynamics

Egbelowo

Munyakazi

Dlamini

et al. 2023

Front. Appl. Math. Stat.

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The co-infection of visceral leishmaniasis (VL) and tuberculosis (TB) patients pose a major public health challenge. In this study, we develop a mathematical model to study the transmission dynamics of VL and TB co-infection by first analyzing the VL and TB sub-models separately. The dynamics of these sub-models and the full co-infection model are determined based on the reproduction number. When the associated reproduction number (R1) for the TB-only model and (R2) for the VL-only are less than unity, the model exhibits backward bifurcation. If max{R1,R2}=R1, then the TB-VL co-infection model exhibits backward bifurcation for values of R1. Furthermore, if max{R1,R2}=R2, and by choosing the transmission probability, βL as the bifurcation parameter, then the phenomenon of backward bifurcation occurs for values of R2. Consequently, the full model, whose associated reproduction number is R0, also exhibits backward bifurcation when R0=1. The equilibrium points and their stability for the models are determined and analyzed based on the magnitude of the respective reproduction numbers. Finally, some numerical simulations are presented to show the reliability of our theoretical results.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Modeling visceral leishmaniasis and tuberculosis co-infection dynamics

Egbelowo

Munyakazi

Dlamini

et al. 2023

Front. Appl. Math. Stat.

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“…Mathematical modelling has been used extensively in studying the behaviour of infectious diseases, including their co-infections [1,7,13,18,23,28,41,43,44]. Particularly, Several mathematical models have been developed to understand the transmission dyanamics of Chlamydia trachomatis infections.…”

Section: Introductionmentioning

confidence: 99%

Optimal Control and Cost-Effectiveness Analysis of an HPV–Chlamydia trachomatis Co-infection Model

2021

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In this work, a co-infection model for human papillomavirus (HPV) and Chlamydia trachomatis with cost-effectiveness optimal control analysis is developed and analyzed. The disease-free equilibrium of the co-infection model is shown not to be globally asymptotically stable, when the associated reproduction number is less unity. It is proven that the model undergoes the phenomenon of backward bifurcation when the associated reproduction number is less than unity. It is also shown that HPV re-infection (ε p = 0) induced the phenomenon of backward bifurcation. Numerical simulations of the optimal control model showed that: (i) focusing on HPV intervention strategy alone (HPV prevention and screening), in the absence of Chlamydia trachomatis control, leads to a positive population level impact on the total number of individuals singly infected with Chlamydia trachomatis, (ii) Concentrating on Chlamydia trachomatis intervention controls alone (Chlamydia trachomatis prevention and treatment), in the absence of HPV intervention strategies, a positive population level impact is observed on the total number of individuals singly infected with HPV. Moreover, the strategy that combines and implements HPV and Chlamydia trachomatis prevention controls is the most cost-effective of all the control strategies in combating the co-infections of HPV and Chlamydia trachomatis.

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“…Some authors, in research papers, studied and analyzed the transmission dynamics of TB diseases in human populations. [2][3][4][5] The main way of the disease progression is either by primary infection (the disease grows after infection) or by endogenous reactivation (many years after infection the disease develops). After primary infection, progressive TB may develop either as a continuation of primary infection or as an endogenous reactivation of a latent focus.…”

Section: Introductionmentioning

confidence: 99%

A fractional‐order model with time delay for tuberculosis with endogenous reactivation and exogenous reinfections

Rajivganthi

Rihan

Alsakaji

2019

Math Methods in App Sciences

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In this paper, we propose a fractional-order delay differential model for tuberculosis (TB) transmission with the effects of endogenous reactivation and exogenous reinfections. We investigate the qualitative behaviors of the model throughout the local stability of the steady states and bifurcation analysis. A discrete time delay is introduced in the model to justify the time taken for diagnosis of the disease. Existence and positivity of the solutions are investigated. Some interesting sufficient conditions that ensure the local asymptotic stability of infection-free and endemic steady states are studied. The fractional-order TB model undergoes Hopf bifurcation with respect to time delay and disease transmission rate. The presence of fractional order and time delay in the model improves the model behaviors and develops the stability results. A numerical example is provided to support our theoretical results.

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Optimal control of intervention strategies in malaria–tuberculosis co-infection with relapse

Cited by 9 publications

References 20 publications

Modeling visceral leishmaniasis and tuberculosis co-infection dynamics

Modeling visceral leishmaniasis and tuberculosis co-infection dynamics

Optimal Control and Cost-Effectiveness Analysis of an HPV–Chlamydia trachomatis Co-infection Model

A fractional‐order model with time delay for tuberculosis with endogenous reactivation and exogenous reinfections

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