No abstract

No abstract

No abstract

No abstract

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, $\beta\sst{cv}$, the parameter accounting for increased susceptibility to COVID-19 by comorbid susceptibles, $\chi\sst{cm}$, the comorbidity development rate, $\theta\sst{cm}$, the detection rate for singly infected and co-infected individuals, $\eta_1$ and $\eta_2$, as well as the recovery rate from COVID-19 for co-infected individuals, $\varphi\sst{i2}$. 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.

No abstract

The re-emergence of syphilis has become a global public health issue, and more persons are getting infected, especially in developing countries. This has also led to an increase in the incidence of human immunodeficiency virus (HIV) infections as some studies have shown in the recent decade. This paper investigates the synergistic interaction between HIV and syphilis using a mathematical model that assesses the impact of syphilis treatment on the dynamics of syphilis and HIV co-infection in a human population where HIV treatment is not readily available or accessible to HIV-infected individuals. In the absence of HIV, the syphilis-only model undergoes the phenomenon of backward bifurcation when the associated reproduction number ([Formula: see text]) is less than unity, due to susceptibility to syphilis reinfection after recovery from a previous infection. The complete syphilis-HIV co-infection model also undergoes the phenomenon of backward bifurcation when the associated effective reproduction number ([Formula: see text]) is less than unity for the same reason as the syphilis-only model. When susceptibility to syphilis reinfection after treatment is insignificant, the disease-free equilibrium of the syphilis-only model is shown to be globally asymptotically stable whenever the associated reproduction number ([Formula: see text]) is less than unity. Sensitivity and uncertainty analysis show that the top three parameters that drive the syphilis infection (with respect to the associated response function, [Formula: see text]) are the contact rate ([Formula: see text]), modification parameter that accounts for the increased infectiousness of syphilis-infected individuals in the secondary stage of the infection ([Formula: see text]) and treatment rate for syphilis-only infected individuals in the primary stage of the infection ([Formula: see text]). The co-infection model was numerically simulated to investigate the impact of various treatment strategies for primary and secondary syphilis, in both singly and dually infected individuals, on the dynamics of the co-infection of syphilis and HIV. It is observed that if concerted effort is exerted in the treatment of primary and secondary syphilis (in both singly and dually infected individuals), especially with high treatment rates for primary syphilis, this will result in a reduction in the incidence of HIV (and its co-infection with syphilis) in the population.

A two-sex deterministic model for Human Papillomavirus (HPV) that assesses the impact of treatment and vaccination on its transmission dynamics is designed and rigorously analyzed. The model is shown to exhibit the phenomenon of backward bifurcation, caused by the imperfect vaccine as well as the re-infection of individuals who recover from a previous infection, when the associated reproduction number is less than unity. Analysis of the reproduction number reveals that the impact of treatment on effective control of the disease is conditional, and depends on the sign of a certain threshold unlike when preventive measures are implemented (i.e. condom use and vaccination of both males and females). Numerical simulations of the model showed that, based on the parameter values used therein, a vaccine (with 75% efficacy) for male population with about 40% condom compliance by females will result in a significant reduction in the disease burden in the population. Also, the numerical simulations of the model reveal that with 70% condom compliance by the male population, administering female vaccine (with 45% efficacy) is sufficient for effective control of the disease.