COVID-19, a novel coronavirus, is a respiratory infection which is spread between humans through small droplets expelled when a person with COVID-19 sneezes, coughs, or speaks. An SEIQR model to investigate the spread of COVID-19 was formulated and analysed. The disease free equilibrium point for formulated model was shown to be globally asymptotically stable. The endemic states were shown to exist provided that the basic reproduction number is greater than unity. By use of Routh-Hurwitz criterion and suitable Lyapunov functions, the endemic states are shown to be locally and globally asymptotically stable respectively. This means that any perturbation of the model by the introduction of infectives the model solutions will converge to the endemic states whenever reproduction number is greater than one, thus the disease transmission levels can be kept quite low or manageable with minimal deaths at the peak times of the re-occurrence.
Human papilloma Virus (HPV) is the primary infection that causes Cervical cancer. Due to the high cost of treatment for cervical cancer, protection against HPV and Cervical cancer infection may be preferable in a scarce resource settings. In this paper, a deterministic model that incorporates protection against the infection was developed and analysed. The endemic state is shown to exist provided that the reproduction number is greater than unity. Furthermore, by the use of Routh-Hurwitz criterion and suitable Lyapunov functions, Endemic Equilibrium (EE) is shown to exist provided that the reproduction number is greater than unity. By use of a suitable Lyapunov function, the endemic state was shown to be globally asymptotically stable. The effectiveness of protection is achieved if well done hence, an increase in protection leads to low disease prevalence in a population.
In this paper a mathematical model describing a between host cervical cancer infection incorporating diagnosis was formulated and analysed. The qualitative analysis of model showed that the infection dynamics can best be described by the threshold value R0B , in which for the value of R0B < 1 the infection free equilibrium is globally asymptotically stable. This implies that we do not expect the disease outbreak for life. Thus, the disease will die out of the population. The endemic states are shown to exist provided that the reproduction number is greater than unity R0B > 1 . By use of Routh-Hurwitz criterion and suitable Lyapunov functions, the endemic states are shown to be locally and globally asymptotically stable respectively. This implies that disease transmission levels can be kept quite low or manageable with minimal deaths at the peak times of the re-occurrences. The numerical results show that the disease related mortality is eradicated if diagnosis is done at an early stage hence late diagnosis increases the risk of cervical cancer infection among the infected individuals.
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