Population dynamics of a mathematical model for syphilis

Iboi, Enahoro; Okuonghae, D.

doi:10.1016/j.apm.2015.09.090

Cited by 31 publications

(27 citation statements)

References 15 publications

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“…The analysis of the model will be performed with β M replaced by the equation in . The model complements other models for syphilis transmission dynamics in the literature (such as those in Garnett et al, Milner and Zhao,, and Iboi and Okuonghae, by, inter alia…”

Section: Model Formulationmentioning

confidence: 71%

“…Rigorous qualitative analysis of the model shows that it undergoes the phenomenon of backward bifurcation when the associated reproduction number of the model (denoted by

R_{0}

) is less than unity. The epidemiological consequence of backward bifurcation, a dynamic phenomenon characterized by the co‐existence of the stable disease‐free equilibrium and a stable endemic equilibrium when

R_{0}

is less than unity, is that the classical epidemiological requirement of bringing (and maintaining)

R_{0}

to a value less than unity, while necessary, is no longer sufficient for the effective control (or elimination) of the disease . In a backward bifurcation situation, effective disease control is dependent on the initial sizes of the subpopulations of the model.…”

Section: Discussionmentioning

confidence: 99%

“…Item (c) of Theorem suggests the existence of multiple endemic equilibria when

R_{0} < 1

(which is typically a signature for the existence of the phenomenon of backward bifurcation. The phenomenon of backward bifurcation, which is characterized by the co‐existence of a stable DFE and a stable endemic equilibrium when the associated reproduction number of the model is less than unity, has been observed in numerous disease transmission models, such as those for (or with) vector‐borne diseases, imperfect vaccination, and multigroups .…”

Section: Mathematical Analysismentioning

confidence: 99%

“…Oxman et al used multicompartment iterative computer simulation with empirically derived input data to simulate and ascertain behavioral and sociological features necessary to produce epidemic transmission. Iboi and Okuonghae designed and analysed a mathematical model for the transmission dynamics of syphilis that incorporates early and late latent stages of syphilis infection, reversions of early latent syphilis to the primary and secondary stages as well as the 3 potential outcomes that emanate from the late latent stage of infection while Saad‐Roy et al developed a deterministic model for syphilis transmission in gay men population. This study presents a new, 2‐group, deterministic, sex‐structured mathematical model for gaining insight into the transmission dynamics of syphilis in a population.…”

Section: Introductionmentioning

confidence: 99%

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Mathematics of a sex‐structured model for syphilis transmission dynamics

Gumel

Lubuma

Sharomi

et al. 2018

Math Methods in App Sciences

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Communicated by: J. Banasiak MSC Classification: 34A34; 37N25; 92B05; 92D30 Syphilis, a major sexually transmitted disease, continues to pose major public health burden in both underdeveloped and developed nations of the world.This study presents a new 2-group sex-structured model for assessing the community-level impact of treatment and condom use on the transmission dynamics and control of syphilis. Rigorous analysis of the model shows that it undergoes the phenomenon of backward bifurcation. In the absence of this phenomenon (which is shown to arise because of the reinfection of recovered individuals), the disease-free equilibrium of the model is shown to be globally asymptotically stable when the associated reproduction number is less than unity. Furthermore, the model can have multiple endemic equilibria when the reproduction threshold exceeds unity. Numerical simulations of the model, using data relevant to the transmission dynamics of the disease in Nigeria, show that, with the assumed 80% condom efficacy, the disease will continue to persist (ie, remain endemic) in the population regardless of the level of compliance in condom usage by men. Furthermore, detailed optimal control analysis (using Pontraygin's maximum principle) reveals that, for situations where the cost of implementing the controls (treatment and condom-use) considered in this study is low, channelling resources to a treatment-only strategy is more effective than channelling them to a condom-use only strategy. Furthermore, as expected, the combined condom-treatment strategy provides a higher population-level impact than the treatment-only strategy or the condom-use only strategy. When the cost of implementing the controls is high, the 3 strategies are essentially equally as ineffective.

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Section: Model Formulationmentioning

confidence: 71%

“…Rigorous qualitative analysis of the model shows that it undergoes the phenomenon of backward bifurcation when the associated reproduction number of the model (denoted by

R_{0}

R_{0}

is less than unity, is that the classical epidemiological requirement of bringing (and maintaining)

R_{0}

Section: Discussionmentioning

confidence: 99%

“…Item (c) of Theorem suggests the existence of multiple endemic equilibria when

R_{0} < 1

Section: Mathematical Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Mathematics of a sex‐structured model for syphilis transmission dynamics

Gumel

Lubuma

Sharomi

et al. 2018

Math Methods in App Sciences

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show abstract

“…For example, Sun showed the dynamical behavior and emergent properties of interacting systems, which highlighted the Allee dynamics in ecology could be widely applicable in fields of epidemiology. Iboi and Okuonghae designed the new nonlinear differential equations for transmission dynamics of syphilis in a population and qualitatively assessed the role of temporary immune deficiency in the transmission process. For single population models, the local stability and bifurcation analysis in Manjunath et al are established in view of Poincar

\overset{e}{true}

normal forms and center manifold theory.…”

Section: Introductionmentioning

confidence: 99%

Local and global Hopf bifurcation in a neutral population model with age structure

Duan

Niu

Wei

2019

Math Methods in App Sciences

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In this paper, an age‐structured population model with the form of neutral functional differential equation is studied. We discuss the stability of the positive equilibrium by analyzing the characteristic equation. Local Hopf bifurcation results are also obtained by choosing the mature delay as bifurcation parameter. On the center manifold, the normal form of the Hopf bifurcation is derived, and explicit formulae for determining the criticality of bifurcation are theoretically given. Moreover, the global continuation of Hopf bifurcating periodic solutions is investigated by using the global Hopf bifurcation theory of neutral equations. Finally, some numerical examples are carried out to support the main results.

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Mathematical Assessment of the Role of Early Latent Infections and Targeted Control Strategies on Syphilis Transmission Dynamics

et al. 2018

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A new multi-stage deterministic model for the transmission dynamics of syphilis, which incorporates disease transmission by individuals in the early latent stage of syphilis infection and the reversions of early latent syphilis to the primary and secondary stages, is formulated and rigorously analysed. The model is used to assess the population-level impact of preventive (condom use) and therapeutic measures (treatment using antibiotics) against the spread of the disease in a community. It is shown that the disease-free equilibrium of the model is globally-asymptotically stable whenever the associated control reproduction number (denoted by [Formula: see text]) is less than unity. A special case of the model is shown to have a unique and globally-asymptotically stable endemic equilibrium whenever the associated reproduction number (denoted by [Formula: see text]) exceeds unity. Uncertainty and sensitivity analysis of the model, using parameter values and ranges relevant to syphilis transmission dynamics in Nigeria, show that the top three parameters that drive the syphilis infection (with respect to [Formula: see text]) are the disease transmission rate ([Formula: see text]), compliance in condom use (c) and efficacy of condom ([Formula: see text]). Numerical simulations of the model show that the targeted treatment of secondary syphilis cases is more effective than the targeted treatment of individuals in the primary or early latent stage of syphilis infection.

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Population dynamics of a mathematical model for syphilis

Cited by 31 publications

References 15 publications

Mathematics of a sex‐structured model for syphilis transmission dynamics

Mathematics of a sex‐structured model for syphilis transmission dynamics

Local and global Hopf bifurcation in a neutral population model with age structure

Mathematical Assessment of the Role of Early Latent Infections and Targeted Control Strategies on Syphilis Transmission Dynamics

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