Mathematical Model and Optimal Control of New-Castle Disease (ND)

Ijeoma, Uwakwe Joy; Chioma, Inyama Simeon; Omame, Andrew

doi:10.11648/j.acm.20200903.14

Cited by 16 publications

(7 citation statements)

References 12 publications

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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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Section: Introductionmentioning

confidence: 99%

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

2021

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“…Lately, mathematical models have been developed to consider the optimal control strategies for the dynamics of infectious diseases including their co-infections [1, 9, 11, 20, 26, 27, 31, 32, 34]. Agusto and Adekunle [1] studied the optimal control and cost-effectiveness analysis of the co-infection of drug-resistant tuberculosis and HIV/AIDS.…”

Section: Introductionmentioning

confidence: 99%

A co-infection model for Oncogenic HPV and TB with Optimal Control and Cost-Effectiveness Analysis

Omame

Okuonghae

2020

Preprint

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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 is shown to exhibit the dynamical property of backward bifurcation when the associated reproduction number is less than unity. Furthermore, it is shown that TB and HPV re-infection parameters (ϕp ≠ 0 and σT ≠ 0) as well as TB exogenous re-infection term (ϵ1 ≠ 0) oncogenic HPV-TB co-infection model. The global asymptotic stability of the disease-free equilibrium of the co-infection model is also proven 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. Uncertainty and global sensitivity analysis are also carried out to determine the top ranked parameters that drive the dynamics of the co-infection model, when the associated reproduction numbers as well as the infected populations are used as response functions. 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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“…Mathematical models have been used extensively in studying the behaviour of infectious diseases [4, 5, 6, 7, 8, 9, 10, 11]. A lot of models have been developed for the dynamics of the co-infections of two diseases [12, 13, 14, 15, 16, 17, 18].…”

Section: Introductionmentioning

confidence: 99%

A co-infection model for Two-Strain Malaria and Cholera with Optimal Control

Egeonu

Inyama

Omame

2020

Preprint

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A mathematical model for two strains of Malaria and Cholera with optimal control is studied and analyzed to assess the impact of treatment controls in reducing the burden of the diseases in a population, in the presence of malaria drug resistance. The model is shown to exhibit the dynamical property of backward bifurcation when the associated reproduction number is less than unity. The global asymptotic stability of the disease-free equilibrium of the model is proven not to exist. The necessary conditions for the existence of optimal control and the optimality system for the model is established using the Pontryagin's Maximum Principle. Numerical simulations of the optimal control model reveal that malaria drug resistance can greatly influence the co-infection cases averted, even in the presence of treatment controls for co-infected individuals.

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Mathematical Model and Optimal Control of New-Castle Disease (ND)

Cited by 16 publications

References 12 publications

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

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

A co-infection model for Oncogenic HPV and TB with Optimal Control and Cost-Effectiveness Analysis

A co-infection model for Two-Strain Malaria and Cholera with Optimal Control

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