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

2020 ◽  
Author(s):  
Kenneth Uzoma Egeonu ◽  
Simeon Chioma Inyama ◽  
Andrew Omame
Keyword(s):  
Optimal Control ◽  
Drug Resistance ◽  
Necessary Conditions ◽  
Reproduction Number ◽  
Dynamical Property ◽  
Backward Bifurcation ◽  
Infection Model ◽  
Existence Of Optimal Control ◽  
The Impact ◽  
Disease Free

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.

scholarly journals Mathematical Analysis of a model for Chlamydia and Gonorrhea Codynamics with Optimal Control

2020 ◽  
Author(s):  
Eziaku Chinomso Chukukere ◽  
Simeon Chioma Inyama ◽  
Andrew Omame
Keyword(s):  
Optimal Control ◽  
Chlamydia Trachomatis ◽  
Necessary Conditions ◽  
Reproduction Number ◽  
Intervention Strategy ◽  
Infection Model ◽  
Control Analysis ◽  
Existence Of Optimal Control ◽  
The Impact ◽  
Disease Free

Abstract A model for Chlamydia trachomatis (CT) and Gonorrhea codynamics, with optimal control analysis is studied and analyzed to assess the impact of targetted treatment for each of the diseases on their co-infections in a population. The model exhibits the dynamical feature of backward bifurcation when the associated reproduction number is less than unity. 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. Simulations of the optimal control model reveal that the intervention strategy which implements female Chlamydia trachomatis treatment and male gonorrhea treatment is the most effective in combating the co-infections of Chlamydia trachomatis and gonorrhea.

scholarly journals Optimal Control and Cost-effectiveness Analysis of an HPV-Chlamydia Trachomatis co-infection model

2020 ◽  
Author(s):  
Andrew Omame ◽  
Celestine Uchenna Nnanna ◽  
Simeon Chioma Inyama
Keyword(s):  
Optimal Control ◽  
Cost Effectiveness ◽  
Chlamydia Trachomatis ◽  
Reproduction Number ◽  
Population Level ◽  
Backward Bifurcation ◽  
Infection Model ◽  
Control Analysis ◽  
Number Of Individuals ◽  
Positive Population

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 \textbf{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 ($\varepsilon\sst{p} \neq 0$) 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.

scholarly journals Mathematical Modeling and Optimal Control Analysis of COVID-19 in Ethiopia

2020 ◽  
Author(s):  
Haileyesus Tessema Alemneh ◽  
Getachew Teshome Telahun
Keyword(s):  
Optimal Control ◽  
Necessary Conditions ◽  
Reproduction Number ◽  
Control Strategies ◽  
Equilibrium Points ◽  
Control Model ◽  
Control Analysis ◽  
Basic Model ◽  
Short Period ◽  
Disease Free

In this paper we developed a deterministic mathematical model of the pandemic COVID-19 transmission in Ethiopia, which allows transmission by exposed humans. We proposed an SEIR model using system of ordinary differential equations. First the major qualitative analysis, like the disease free equilibruim point, endemic equilibruim point, basic reproduction number, stability analysis of equilibrium points and sensitivity analysis was rigorously analysed. Second, we introduced time dependent controls to the basic model and extended to an optimal control model of the disease. We then analysed using Pontryagins Maximum Principle to derive necessary conditions for the optimal control of the pandemic. The numerical simulation indicated that, an integrated strategy effective in controling the epidemic and the gvernment must apply all control strategies in combating COVID-19 at short period of time.

TRANSMISSION DYNAMICS AND OPTIMAL CONTROL OF AN INFLUENZA MODEL WITH QUARANTINE AND TREATMENT

2012 ◽  
Vol 05 (03) ◽  
pp. 1260011 ◽  
Author(s):  
WEI-WEI SHI ◽  
YUAN-SHUN TAN
Keyword(s):  
Optimal Control ◽  
Disease Transmission ◽  
Reproduction Number ◽  
Influenza Pandemic ◽  
Control Measures ◽  
Globally Asymptotically Stable ◽  
Number Formula ◽  
Parameter Values ◽  
The Impact ◽  
Disease Free

We develop an influenza pandemic model with quarantine and treatment, and analyze the dynamics of the model. Analytical results of the model show that, if basic reproduction number [Formula: see text], the disease-free equilibrium (DFE) is globally asymptotically stable, if [Formula: see text], the disease is uniformly persistent. The model is then extended to assess the impact of three anti-influenza control measures, precaution, quarantine and treatment, by re-formulating the model as an optimal control problem. We focus primarily on controlling disease with a possible minimal the systemic cost. Pontryagin's maximum principle is used to characterize the optimal levels of the three controls. Numerical simulations of the optimality system, using a set of reasonable parameter values, indicate that the precaution measure is more effective in reducing disease transmission than the other two control measures. The precaution measure should be emphasized.

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

2020 ◽  
Author(s):  
Andrew Omame ◽  
Daniel Okuonghae
Keyword(s):  
Optimal Control ◽  
Cost Effectiveness ◽  
Reproduction Number ◽  
Intervention Strategy ◽  
Cost Effectiveness Analysis ◽  
Infection Model ◽  
Tb Treatment ◽  
Effectiveness Analysis ◽  
The Impact ◽  
Oncogenic Hpv

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.

scholarly journals Assessing the Potential Impact of Immunity Waning on the Dynamics of COVID-19: An Endemic Model of COVID-19

2021 ◽  
Author(s):  
MUSA RABIU ◽  
Sarafa A. Iyaniwura
Keyword(s):  
Disease Transmission ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Backward Bifurcation ◽  
Disease Dynamics ◽  
Potential Impact ◽  
The Impact ◽  
Induced Immunity ◽  
Disease Free ◽  
Pharmaceutical Interventions

Abstract We developed an endemic model of COVID-19 to assess the impact of vaccination and immunity waning on the dynamics of the disease. Our model exhibits the phenomenon of backward bifurcation and bi-stability, where a stable disease-free equilibrium co-exists with a stable endemic equilibrium. The epidemiological implication of this is that the control reproduction number being less than unity is no longer sufficient to guarantee disease eradication. We showed that this phenomenon could be eliminated by either increasing the vaccine efficacy or by reducing the disease transmission rate (adhering to non-pharmaceutical interventions). Furthermore, we numerically investigated the impacts of vaccination and waning of both vaccine-induced immunity and post-recovery immunity on the disease dynamics. Our simulation results show that the waning of vaccine-induced immunity has more effect on the disease dynamics relative to post-recovery immunity waning, and suggests that more emphasis should be on reducing the waning of vaccine-induced immunity to eradicate COVID-19.

scholarly journals A co-infection model for HPV and syphilis with optimal control and cost-effectiveness analysis

2021 ◽  
pp. 2150050
Author(s):  
A. Omame ◽  
D. Okuonghae ◽  
U. E. Nwafor ◽  
B. U. Odionyenma
Keyword(s):  
Optimal Control ◽  
Cost Effectiveness ◽  
Reproduction Number ◽  
Infection Model ◽  
Contact Rate ◽  
Demographic Parameter ◽  
Effective Contact ◽  
Number Formula ◽  
Syphilis Treatment ◽  
Disease Free

A co-infection model for human papillomavirus (HPV) and syphilis with cost-effectiveness optimal control analysis is developed and presented. The full co-infection model is shown to undergo the phenomenon of backward bifurcation when a certain condition is satisfied. The global asymptotic stability of the disease-free equilibrium of the full model is shown not to exist when the associated reproduction number is less than unity. The existence of endemic equilibrium of the syphilis-only sub-model is shown to exist and the global asymptotic stability of the disease-free and endemic equilibria of the syphilis-only sub-model was established, for a special case. Sensitivity analysis is also carried out on the parameters of the model. Using the syphilis associated reproduction number, [Formula: see text], as the response function, it is observed that the five-ranked parameters that drive the dynamics of the co-infection model are the demographic parameter [Formula: see text], the effective contact rate for syphilis transmission, [Formula: see text], the progression rate to late stage of syphilis [Formula: see text], and syphilis treatment rates: [Formula: see text] and [Formula: see text] for co-infected individuals in compartments [Formula: see text] and [Formula: see text], respectively. Moreover, when the HPV associated reproduction number, [Formula: see text], is used as the response function, the five most dominant parameters that drive the dynamics of the model are the demographic parameter [Formula: see text], the effective contact rate for HPV transmission, [Formula: see text], the fraction of HPV infected who develop persistent HPV [Formula: see text], the fraction of individuals vaccinated against incident HPV infection [Formula: see text] and the HPV vaccine efficacy [Formula: see text]. Numerical simulations of the optimal control model showed that the optimal control strategy which implements syphilis treatment controls for singly infected individuals is the most cost-effective of all the control strategies in reducing the burden of HPV and syphilis co-infections.

scholarly journals Impact of Treatment on HIV-Malaria CoInfection Based on Mathematical Modeling

2019 ◽  
Vol 39 ◽  
pp. 45-62
Author(s):  
Amit Kumar Saha ◽  
Ashrafi Meher Niger ◽  
Chandra Nath Podder
Keyword(s):  
Treatment Strategy ◽  
Reproduction Number ◽  
Treatment Strategies ◽  
Backward Bifurcation ◽  
Asymptotically Stable ◽  
Single Treatment ◽  
Globally Asymptotically Stable ◽  
Mixed Treatment ◽  
The Impact ◽  
Disease Free

The distribution of HIV and malaria overlap globally. So there is always a chance of co-infection. In this paper the impact of medication on HIV-Malaria co-infection has been analyzed and we have developed a mathematical model using the idea of the models of Mukandavire, et al. [13] and Barley, et al. [3] where treatment classes are included. The disease-free equilibrium (DFE) of the HIV-only model is globally-asymptotically stable (GAS) when the reproduction number is less than one. But it is shown that in the malaria-only model, there is a coexistence of stable disease-free equilibrium and stable endemic equilibrium, for a certain interval of the reproduction number less than unity. This indicates the existence of backward bifurcation. Numerical simulations of the full model are performed to determine the impact of treatment strategies. It is shown that malaria-only treatment strategy reduces more new cases of the mixed infection than the HIV-only treatment strategy. Moreover, mixed treatment strategy reduces the least number of new cases compared to single treatment strategies. GANIT J. Bangladesh Math. Soc.Vol. 39 (2019) 45-62

scholarly journals Stochastic Optimal Control Model of Haemorrhagic Conjunctivitis Disease

2019 ◽  
pp. 1-19
Author(s):  
Sacrifice Nana-Kyere ◽  
Desmond Titus Banon ◽  
Seth N. Marmah ◽  
Daniel Kwarteng
Keyword(s):  
Optimal Control ◽  
Control Strategy ◽  
Necessary Conditions ◽  
Reproduction Number ◽  
Control Model ◽  
Optimum Control ◽  
Stochastic Perturbations ◽  
Stochastic Version ◽  
Research Article ◽  
Existence Of Optimal Control

In this research article, a model for the transmission dynamics of haemorrhagic conjunctivitis disease is presented. The tool of dynamical system is employed in investigating the potency of the spreading of the epidemic. The analysis revealed the likelihood of the epidemic to spread when the basic reproduction number exceeds one. The model is reformulated as optimal control problem to assess the effectiveness of the proposed control strategy. Maximum Principle was employed to derive the necessary conditions for the existence of optimal control. Numerical solution of the optimality was derived and computed to investigate the optimum control strategy that would be efficacious to be implemented in reducing the number of exposed and infected individuals. Stochastic version of the model is deduced by introducing stochastic perturbations in the deterministic one. Numerical simulations are provided to illustrate the differences in the dynamics of the models and to understand the epidemic phenomenon.

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