Backward bifurcation and hysteresis in models of recurrent tuberculosis

Wangari, Isaac Mwangi; Stone, Lewi

doi:10.1371/journal.pone.0194256

Cited by 32 publications

(30 citation statements)

References 48 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Selecting parameters such that σ 2 = σ 3 = 0.125, and σ 1 = 0.25 while other parameters remain at baseline values, results in Fig 5A , which shows a hysteresis phenomenon. Hysteresis implies that multiple equilibria, both stable and unstable, occur simultaneously above the epidemic threshold R 0 = 1 (see [ 62 , 63 ]). In Fig 5A the unstable equilibrium is marked by a red dotted line that separates two stable equilibria: low endemic and high endemic.…”

Section: The Impact Of Reinfection Parameters σ mentioning

confidence: 99%

Modelling heterogeneity in host susceptibility to tuberculosis and its effect on public health interventions

Wangari¹,

Trauer

Stone

2018

PLoS ONE

Self Cite

View full text Add to dashboard Cite

A tuberculosis (TB) model that accounts for heterogeneity in host susceptibility to tuberculosis is proposed, with the aim of investigating the implications this may have for the effectiveness of public health interventions. The model examines the possibility that recovered individuals treated from active TB and individuals treated with preventive therapy acquire different levels of immunity. This contrasts with recent studies that assume the two cohorts acquire the same level of immunity, and therefore both groups are reinfected at the same rate. The analysis presented here examines the impact of this assumption when designing intervention strategies. Comparison of reinfection rates between cohorts treated with preventive therapy and recovered individuals who were previously treated for active TB provides important epidemiological insights. It is found that the reinfection rate of the cohort treated with preventive therapy is the one that plays the key role in qualitative changes in TB dynamics. By contrast, the reinfection rate of recovered individuals (previously treated from active TB) plays a minor role. Moreover, the study shows that preventive treatment of individuals during early latency is always beneficial regardless of the level of susceptibility to reinfection. Further, if patients have greater immunity following treatment for late latent infection, then treatment is again beneficial. However, if susceptibility increases following treatment for late latent infection, the effect of treatment depends on the epidemiological setting. That is: (i) in (very) low burden settings, the effect on reactivation predominates and the burden declines with treatment; (ii) in moderate to high burden settings the effect of reinfection predominates and burden increases with treatment. The effect is most dominant between the two reinfection thresholds, RT2 and RT1, respectively associated with individuals being treated with preventive therapy and individuals with untreated late latent TB infection.

show abstract

Section: The Impact Of Reinfection Parameters σ mentioning

confidence: 99%

Modelling heterogeneity in host susceptibility to tuberculosis and its effect on public health interventions

Wangari¹,

Trauer

Stone

2018

PLoS ONE

Self Cite

View full text Add to dashboard Cite

show abstract

“…Hence, the bifurcation deriving from the disease-free equilibrium to an endemic equilibrium is forward. However, as of recent years, the backward bifurcation phenomenon has emerged in research on infection control (see [28,38,41]). In this situation, the basic reproduction number cannot accurately illustrate the important disease eradication any longer.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…The backward bifurcation phenomenon offers an alternate interpretation, as it demonstrates that, even though R 0 < 1 and the DFE is steady, another steady endemic equilibrium can still coexist simultaneously [28,41]. Therefore, even though R 0 < 1, a population could be at an endemic equilibrium wherein the infection persists indefinitely [41]. When several stable equilibria coexist simultaneously, the final equilibrium that a population will reach relies upon the initial conditions (i.e., regarding the number of people) of its subpopulations [41].…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, even though R 0 < 1, a population could be at an endemic equilibrium wherein the infection persists indefinitely [41]. When several stable equilibria coexist simultaneously, the final equilibrium that a population will reach relies upon the initial conditions (i.e., regarding the number of people) of its subpopulations [41].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An SVEIRE Model of Tuberculosis to Assess the Effect of an Imperfect Vaccine and Other Exogenous Factors

2021

View full text Add to dashboard Cite

This study extends a deterministic mathematical model for the dynamics of tuberculosis transmission to examine the impact of an imperfect vaccine and other exogenous factors, such as re-infection among treated individuals and exogenous re-infection. The qualitative behaviors of the model are investigated, covering many distinct aspects of the transmission of the disease. The proposed model is observed to show a backward bifurcation, even when Rv<1. As such, we assume that diminishing Rv to less than unity is not effective for the elimination of tuberculosis. Furthermore, the results reveal that an imperfect tuberculosis vaccine is always effective at reducing the spread of infectious diseases within the population, though the general effect increases with the increase in effectiveness and coverage. In particular, it is shown that a limited portion of people being vaccinated at steady-state and vaccine efficacy assume a equivalent role in decreasing disease burden. From the numerical simulation, it is shown that using an imperfect vaccine lead to effective control of tuberculosis in a population, provided that the efficacy of the vaccine and its coverage are reasonably high.

show abstract

Mathematical analysis of the dynamics of a fractional‐order tuberculosis epidemic in a patchy environment under the influence of re‐infection

Jabbari,

Lotfi,

Kheiri

et al. 2023

Math Methods in App Sciences

View full text Add to dashboard Cite

In human societies, memory has a significant impact on the procedure of progression and control of epidemics. Therefore, fractional differential equations govern an epidemic model, including the memory effect. Since infectious diseases can spread from one place to another, human movement impacts the prevalence of such diseases. In this study, we present a two‐patch model for tuberculosis with fractional order and exogenous re‐infection, in which susceptible individuals can move without any obstacle between the patches. The present work establishes the effect of population movement and the backward bifurcation phenomenon on the prevalence of the tuberculosis epidemic with fractional‐order derivatives. Furthermore, to show that the proposed model has backward bifurcation, we provide some conditions between the model's parameters, so in this case, the model of tuberculosis has numerous boundary points. We show the tuberculosis model can exhibit backward bifurcation neither in case of exogenous re‐infection, with some conditions, nor in the situation that the model is vacant from any re‐infection. In contrast, the disease‐free equilibrium of the model is globally asymptotically stable when . Furthermore, we investigate the fractional‐order derivative on the spread of infection. The results show that can perform the function of adventure or expertise of people about the disease background.

show abstract

Backward bifurcation and hysteresis in models of recurrent tuberculosis

Cited by 32 publications

References 48 publications

Modelling heterogeneity in host susceptibility to tuberculosis and its effect on public health interventions

Modelling heterogeneity in host susceptibility to tuberculosis and its effect on public health interventions

An SVEIRE Model of Tuberculosis to Assess the Effect of an Imperfect Vaccine and Other Exogenous Factors

Mathematical analysis of the dynamics of a fractional‐order tuberculosis epidemic in a patchy environment under the influence of re‐infection

Contact Info

Product

Resources

About