A THEORETICAL STUDY ON SCHISTOSOMIASIS INFECTION MODEL: APPLICATION OF BIOLOGICAL OPTIMAL CONTROL

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.

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Analysis of COVID-19 and comorbidity co-infection Model with Optimal Control

10.1101/2020.08.04.20168013 ◽

2020 ◽

Cited By ~ 1

Author(s):

Andrew Omame ◽

Ndolane Sene ◽

Ikenna Nometa ◽

Cosmas Ifeanyi Nwakanma ◽

Emmanuel Ugochukwu Nwafor ◽

...

Keyword(s):

Optimal Control ◽

Detection Rate ◽

Control Strategies ◽

Cost Effective ◽

Cerebrovascular Diseases ◽

Infection Model ◽

Infection Rates ◽

Effective Contact ◽

Using Data ◽

Increased Susceptibility

The new coronavirus disease 2019 (COVID-19) infection is a double challenge for people infected with comorbidities such as cardiovascular and cerebrovascular diseases and diabetes. Comorbidities have been reported to be risk factors for the complications of COVID-19. In this work, we develop and analyze a mathematical model for the dynamics of COVID-19 infection in order to assess the impacts of prior comorbidity on COVID-19 complications and COVID-19 re-infection. The model is simulated using data relevant to the dynamics of the diseases in Lagos, Nigeria, making predictions for the attainment of peak periods in the presence or absence of comorbidity. The model is shown to undergo the phenomenon of backward bifurcation caused by the parameter accounting for increased susceptibility to COVID-19 infection by comorbid susceptibles as well as the rate of re-infection by those who have recovered from a previous COVID-19 infection. Sensitivity analysis of the model when the population of individuals co-infected with COVID-19 and comorbidity is used as response function revealed that the top ranked parameters that drive the dynamics of the co-infection model are the effective contact rate for COVID-19 transmission, βcv, the parameter accounting for increased susceptibility to COVID-19 by comorbid susceptibles, χcm, the comorbidity development rate, θcm, the detection rate for singly infected and co-infected individuals, η1 and η2, as well as the recovery rate from COVID-19 for co-infected individuals, ϕi2. Simulations of the model reveal that the cumulative confirmed cases (without comorbidity) may get up to 180,000 after 200 days, if the hyper susceptibility rate of comorbid susceptibles is as high as 1.2 per day. Also, the cumulative confirmed cases (including those co-infected with comorbidity) may be as high as 1000,000 cases by the end of November, 2020 if the re-infection rates for COVID-19 is 0.1 per day. It may be worse than this if the re-infection rates increase higher. Moreover, if policies are strictly put in place to step down the probability of COVID-19 infection by comorbid susceptibles to as low as 0.4 per day and step up the detection rate for singly infected individuals to 0.7 per day, then the reproduction number can be brought very low below one, and COVID-19 infection eliminated from the population. In addition, optimal control and cost-effectiveness analysis of the model reveal that the the strategy that prevents COVID-19 infection by comorbid susceptibles has the least ICER and is the most cost-effective of all the control strategies for the prevention of COVID-19.

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

10.1101/2020.08.18.20177329 ◽

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.

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