Stability analysis of a delayed HIV-TB co-infection model in resource limitation settings

Tanvi,; Aggarwal, Rajiv

doi:10.1016/j.chaos.2020.110138

Cited by 22 publications

(12 citation statements)

References 18 publications

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“…For example, in tuberculosis (TB), even a minor illness may cause the infection to reactivate. Recent years it has been observed that the COVID-19 disease becomes more deadly to those having already long-term infection like tuberculosis (TB) [9] also HIV with TB shows deadly effect as co-infection [33]. Simultaneously, few studies look at the interaction of two or more diseases.…”

Section: Introductionmentioning

confidence: 99%

Co-infection dynamics of two short term diseases with effect of recovery delay

Tomar¹,

Dhar²,

Kumar³

2022

J. Math. Computer Sci.

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A co-infection model with two short-term diseases with delay in recovery is proposed. Here, we consider the simultaneous transmission of infection does not happen but of simultaneous recovery from both illnesses. The system consists of four epidemiological classes populations, namely: susceptible (S), an infected class with the first disease (I 1 ), an infected class with the second disease (I 2 ), co-infected class (I 12 ). We have found all possible equilibrium states, and the basic reproduction number also examined their stability without and with delay. Analytically, we have established that the local stability of equilibrium points depends on the basic reproduction number in the absence of recovery delay. But with delay, it requires some additional conditions. We have also checked the effect of delay on stability of endemic steady state numerically and showed that beyond a critical threshold value of delay parameter, the system loses its stability, and Hopf bifurcation occurs. Finally, a numerical simulation presented supports the analytical findings.

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Section: Introductionmentioning

confidence: 99%

Co-infection dynamics of two short term diseases with effect of recovery delay

Tomar¹,

Dhar²,

Kumar³

2022

J. Math. Computer Sci.

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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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“…6,7 Mathematical models have been applied extensively in the study of the dynamics of infectious diseases. [8][9][10][11][12][13][14][15] Particularly, models have recently been studied to understand the transmission dynamics of HPV infection (See Omame et al 16 and the references included therein). For instance, Malik et al 17 investigated an optimal control model for HPV, incorporating optimal vaccination strategies for females in the population.…”

Section: Introductionmentioning

confidence: 99%

A co‐infection model for oncogenic human papillomavirus and tuberculosis with optimal control and Cost‐Effectiveness Analysis

Omame

Okuonghae

2021

Optim Control Appl Methods

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A co-infection model for oncogenic human papillomavirus (HPV) and tuberculosis (TB), with optimal control and cost-effectiveness analysis is studied and analyzed to assess the impact of controls against incident infection and against infection with HPV by TB-infected individuals as well as optimal TB treatment in reducing the burden of the co-infection of the two diseases in a population. The co-infection model exhibits backward bifurcation when the associated reproduction number is less than unity. Furthermore, it is shown that TB and HPV re-infection parameters ( p ≠ 0 and t ≠ 0) as well as TB exogenous re-infection term ( 1 ≠ 0) induced the phenomenon of backward bifurcation in the oncogenic HPV-TB co-infection model. The global asymptotic stability of the disease-free equilibrium of the co-infection model is shown not to exist, when the associated reproduction number is below unity. The necessary conditions for the existence of optimal control and the optimality system for the co-infection model is established using the Pontryagin's Maximum Principle. Numerical simulations of the optimal control model reveal that the intervention strategy which combines and implements control against HPV infection by TB infected individuals as well as TB treatment control for dually infected individuals is the most cost-effective of all the control strategies for the control and management of the burden of oncogenic HPV and TB co-infection.

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Stability analysis of a delayed HIV-TB co-infection model in resource limitation settings

Cited by 22 publications

References 18 publications

Co-infection dynamics of two short term diseases with effect of recovery delay

Co-infection dynamics of two short term diseases with effect of recovery delay

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

A co‐infection model for oncogenic human papillomavirus and tuberculosis with optimal control and Cost‐Effectiveness Analysis

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