Mathematical analysis and optimal control interventions for sex structured syphilis model with three stages of infection and loss of immunity

Momoh, Abdulfatai Atte; Bala, Yusuf; Washachi, Dekera Jacob; Dione, Déthié

doi:10.1186/s13662-021-03432-7

Cited by 10 publications

(7 citation statements)

References 35 publications

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“…Under [22], we conclude that the a priori boundedness of the state system, the adjoint system, is how we could establish the uniqueness of the optimality system based on standard control arguments including the bound on the controls (33) and (34). The length of the time ½0, t f is constrained in order to ensure the uniqueness of the optimality system [5].…”

Section: Abstract and Applied Analysismentioning

confidence: 99%

“…To prevent the negative effects of drug resistance, the WHO advises using antiviral medications with a high barrier to resistance (either tenofovir or entecavir) as the preferred first-line treatment [4]. Chronic HBV infection can be treated, although it is not curative [5]. It can prevent or postpone the development of cirrhosis, lower the risk of developing hepatocellular carcinoma (HCC), and increase survival through long-term viral suppression.…”

Section: Introductionmentioning

confidence: 99%

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On the Optimal Control of Intervention Strategies for Hepatitis B Model

Atte

Audu

Dione

et al. 2023

Abstract and Applied Analysis

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Hepatitis B is one of the leading causes of morbidity and mortality, affecting hundreds of millions of people worldwide. Thus, this paper focuses on three control measures as the best way to intervene against the hepatitis B viral infection. These measures are condom use, testing and treatment, and vaccination to stop the disease from spreading over a community. The model comprises seven (7) compartments that include susceptible individuals, latent individuals, acute-infected individuals, chronic-infected individuals, infected by carrier individuals, recovered individuals from the disease, and the vaccinated population. We mathematically established a nonlinear differential equation to study the dynamics of the model. The disease-free equilibrium (DFE) and endemic equilibrium (EE) are reached. The basic reproduction numbers, R 0 A , R 0 H , and R 0 C , determine the transmission of the disease and thus are gotten. We perform sensitivity analysis on the reproduction numbers to identify the factors that affect the reproduction numbers. The results of the sensitivity analysis paved a way for introducing a controlled system which was solved using Pontryagin’s maximum principle (PMP) and the optimality system got. The optimality system was then solved numerically using the forward and backward sweep approach, and graphs were generated, establishing the conditions for local and global stability of the disease-free equilibrium using the Routh-Hurwitz criterion and Castillo-Chavez approach, respectively. We also used Pontryagin’s maximum principle to determine the optimality system. The result of the analysis of the stability of the disease-free equilibrium states that hepatitis B virus can be completely wiped out if the rate of infection is kept at a number less than unity. A numerical simulation of the model was carried out and showed that hepatitis B virus transmission can best be controlled when condom use, testing and treatment, and vaccination are implemented.

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Section: Abstract and Applied Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the Optimal Control of Intervention Strategies for Hepatitis B Model

Atte

Audu

Dione

et al. 2023

Abstract and Applied Analysis

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“…Syphilis is a major sexually transmitted disease and has been affecting millions of individuals both in low-and high-income countries of the world [10]. It is a chronic systemic disease caused by Treponema pallidum bacterium which is mainly transmitted through sex, blood contact, and mother-to-child during birth [4,[10][11][12][13][14][15][16]. Diagnosis, treatment, and using a condom are the basic control mechanisms of syphilis spreading in the community [10].…”

Section: Introductionmentioning

confidence: 99%

“…It can be a cause of different cardiovascular and neurological diseases [17]. Approximately 90% of new syphilis substantial morbidity and mortality data are recorded in low-income countries around the world [11,16]. Co-infection is an infection of an individual with two or more microorganisms' species [20,21].…”

Section: Introductionmentioning

confidence: 99%

COVID-19 and syphilis co-dynamic analysis using mathematical modeling approach

Teklu

Terefe²

2023

Front. Appl. Math. Stat.

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In this study, we have proposed and analyzed a new COVID-19 and syphilis co-infection mathematical model with 10 distinct classes of the human population (COVID-19 protected, syphilis protected, susceptible, COVID-19 infected, COVID-19 isolated with treatment, syphilis asymptomatic infected, syphilis symptomatic infected, syphilis treated, COVID-19 and syphilis co-infected, and COVID-19 and syphilis treated) that describes COVID-19 and syphilis co-dynamics. We have calculated all the disease-free and endemic equilibrium points of single infection and co-infection models. The basic reproduction numbers of COVID-19, syphilis, and COVID-19 and syphilis co-infection models were determined. The results of the model analyses show that the COVID-19 and syphilis co-infection spread is under control whenever its basic reproduction number is less than unity. Moreover, whenever the co-infection basic reproduction number is greater than unity, COVID-19 and syphilis co-infection propagates throughout the community. The numerical simulations performed by MATLAB code using the ode45 solver justified the qualitative results of the proposed model. Moreover, both the qualitative and numerical analysis findings of the study have shown that protections and treatments have fundamental effects on COVID-19 and syphilis co-dynamic disease transmission prevention and control in the community.

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“…With an interest in the optimal control between primary and secondary infection. There are many studies about applying to solve the optimal control problem of dengue fever [28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Local and Global Stability Analysis of Dengue Disease with Vaccination and Optimal Control

et al. 2021

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Dengue fever is a disease that has spread all over the world, including Thailand. Dengue is caused by a virus and there are four distinct serotypes of the virus that cause dengue DENV-1, DENV-2, DENV-3, and DENV-4. The dengue viruses are transmitted by two species of the Aedes mosquitoes, the Aedes aegypti, and the Aedes albopictus. Currently, the dengue vaccine used in Thailand is chimeric yellow tetravalent dengue (CYD-TDV). This research presents optimal control which studies the vaccination only in individuals with a documented past dengue infection (seropositive), regardless of the serotypes of infection causing the initial infection by the disease. The analysis of dengue transmission model is used to establish the local asymptotically stabilities. The property of symmetry in the Lyapunov function an import role in achieving this global asymptotically stabilities. The optimal control systems are shown in numerical solutions and conclusions. The result shows that the control resulted in a significant reduction in the number of infected humans and infected vectors.

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Mathematical analysis and optimal control interventions for sex structured syphilis model with three stages of infection and loss of immunity

Cited by 10 publications

References 35 publications

On the Optimal Control of Intervention Strategies for Hepatitis B Model

On the Optimal Control of Intervention Strategies for Hepatitis B Model

COVID-19 and syphilis co-dynamic analysis using mathematical modeling approach

Local and Global Stability Analysis of Dengue Disease with Vaccination and Optimal Control

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