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

A non-linear mathematical model for analysing the impact of COVID-19 disease on higher education in developing countries

This study proposes a non-linear mathematical model for analysing the effect of COVID-19 dynamics on the student population in higher education institutions. The theory of positivity and boundedness of solution is used to investigate the well-posedness of the model. The disease-free equilibrium solution is examined analytically. The next-generation operator method calculates the basic reproduction number ( R 0 ) . Sensitivity analyses are carried out to determine the relative importance of the model parameters in spreading COVID-19. In light of the sensitivity analysis results, the model is further extended to an optimal control problem by introducing four time-dependent control variables: personal protective measures, quarantine (or self-isolation), treatment, and management measures to mitigate the community spread of COVID-19 in the population. Simulations evaluate the effects of different combinations of the control variables in minimizing COVID-19 infection. Moreover, a cost-effectiveness analysis is conducted to ascertain the most effective and least expensive strategy for preventing and controlling the spread of COVID-19 with limited resources in the student population.

The effect of public health awareness and behaviors on the transmission dynamics of syphilis in Northwest China, 2006-2018, based on a multiple-stages mathematical model

Syphilis, a sexually transmitted infectious disease caused by the bacterium treponema pallidum, has re-emerged as a global public health issue with an estimated 12 million people infected each year. Understanding the impacts of health awareness and behaviors on transmission dynamics of syphilis can help to establish optimal control strategy in different regions. In this paper, we develop a multiple-stage SIRS epidemic model taking into account the public health awareness and behaviors of syphilis. First, the basic reproduction number R0 is obtained, which determines the global dynamics behaviors of the model. We derive the necessary conditions for implementing optimal control and the corresponding optimal solution for mitigation syphilis by using Pontryagin's Maximum Principle. Based on the data of syphilis in Ningxia from 2006 to 2018, the parameterizations and model calibration are carried out. The fitting results are in good agreement with the data. Moreover, sensitivity analysis shows that the public awareness induced protective behaviors C_e, compliance of condom-induced preventability ε and treatment for the primary syphilis m₁ play an important role in mitigating the risk of syphilis outbreaks. These results can help us gain insights into the epidemiology of syphilis and provide guidance for the public health authorities to implement health education programs.

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

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 ([Formula: see text]) 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 C. trachomatis control, leads to a positive population level impact on the total number of individuals singly infected with C. trachomatis, (ii) Concentrating on C. trachomatis intervention controls alone (C. 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 C. trachomatis prevention controls is the most cost-effective of all the control strategies in combating the co-infections of HPV and C. trachomatis.

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

In this study, we develop a nonlinear ordinary differential equation to study the dynamics of syphilis transmission incorporating controls, namely prevention and treatment of the infected males and females. We obtain syphilis-free equilibrium (SFE) and syphilis-present equilibrium (SPE). We obtain the basic reproduction number, which can be used to control the transmission of the disease, and thus establish the conditions for local and global stability of the syphilis-free equilibrium. The stability results show that the model is locally asymptotically stable if the Routh-Hurwitz criteria are satisfied and globally asymptotically stable. The bifurcation analysis result reveals that the model exhibits backward bifurcation. We adopted Pontryagin's maximum principle to determine the optimality system for the syphilis model, which was solved numerically to show that syphilis transmission can be optimally best control using a combination of condoms usage and treatment in the primary stage of infection in both infected male and female populations.

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

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.

Estimating the syphilis incidence and diagnosis rate in Japan: a mathematical modelling study

OBJECTIVES

The reported number of syphilis cases is increasing in Japan. In this study, we aimed to estimate both the incidence of infection and diagnosis-and-reporting rate using a mathematical model that captures the time course of infection.

METHODS

We analysed yearly notification data from 1961 to 2016 and stratified according to clinical stage and sex. We built a compartmental ordinary differential equations model to describe the natural epidemiological course of syphilis in which the incidence of infection and diagnosis-and-reporting rate were included as time-varying parameters that we estimated via the maximum likelihood method.

RESULTS

From 2008 to 2016, the estimated number of new syphilis cases among men and women was 1070 (95% CI 1037 to 1104) and 302 (95% CI 287 to 318), respectively, which was increased from the previous period (1999-2007) with 269 (95% CI 256 to 282) and 71 (95% CI 64 to 78) cases, respectively. The diagnosis-and-reporting rate did not vary greatly over time. We estimated the number of undiagnosed syphilis cases from either incubating or early clinical (ie, primary or secondary) infections in 2016 to be 262 (95% CI 249 to 275) and 79 (95% CI 74 to 84) for men and women, respectively.

CONCLUSIONS

The recent increase in reported cases of syphilis is owing to an increase in the number of infections. We found no evidence of time-dependent improvement in detection or reporting.