Presently, an ongoing outbreak of the monkeypox virus infection that began in Bayelsa State of Nigeria has now spread to other parts of the country including mostly States in the South-South with the Nigerian Ministry of Health confirming 4 samples out of the 43 sent for testing at WHO Regional Laboratory in Dakar, Senegal. This reminds us that apart from the eradicated smallpox, there are other poxviruses that pose potential threat to people in West and Central Africa. In this paper, we developed a mathematical model for the dynamics of the transmission of monkeypox virus infection with control strategies of combined vaccine and treatment interventions. Using standard approaches, we established two equilibria for the model namely: disease-free and endemic. The disease-free equilibrium was proved to be both locally and globally asymptotically stable if 0 1 R < using the next-generation matrix and the comparison theorem. While the endemic equilibrium point existed only when 0 1 R > , was proved to be locally asymptotically stable if 0 1 R > using the linearization plus row-reduction method. The basic reproduction numbers for the humans and the non-human primates of the model are computed using parameter values to tions carried out on the model revealed that the infectious individuals in the human and non-human primates' populations will die out in the course of the proposed interventions in this paper during the time of the study. Sensitivity analysis carried out on the model parameters shows that the basic reproduction numbers of the model which served as a threshold for measuring new infections in the host populations decrease with increase in the control parameters of vaccination and treatment.
Neisseria gonorrhea infection; a sexually transmitted disease, is caused primarily by a type of germ; a bacteria called neisseria gonorrhea. The infection is a major public health challenge today due to the high incidence of infections accompanied by a dwindling number of treatment options especially in developing and underdeveloped countries. In this paper, we developed a mathematical model for the transmission dynamics of neisseria gonorrhea infection and studied the effect of natural immunity and treatment as the only available control interventions on the spread of the disease in a population. We computed the model disease-free equilibrium and analyzed its local and global stability in a well-defined positively invariant and attracting set Ω using the next-generation matrix plus linearization method and the comparison theorem respectively. The disease-free equilibrium was proved to be both locally and globally asymptotically stable if $R_0<1$ and unstable if $R_0>1$. We conducted sensitivity analysis of parameters in the basic reproduction number $R_0$ using the normalized forward sensitivity index method. Results of the analysis revealed that $R_0$ decreases with increase in treatment and natural immunity rates. The results of the numerical simulations carried out using MATLAB R2012B showed that there is increase in new infections due to increased contact with infected individuals in the susceptible population and that, with increased treatment rate and controlled death due to the disease in the population, neisseria gonorrhea infection would be wiped out within 300 days of the treatment intervention.
In this paper, we studied the transmission dynamics of ZIKV in the presence of a vector under the combined effects of treatment and vaccination in a hypothetical population. The disease-free ε and endemic 1 ε equilibria were established with local stability on ε . We established the basic reproduction number R which served as a threshold for measuring the spread of the infection in the population using the next-generation matrix and computed its numerical value to be 0.0185903201 R = using the parameter values. It was established that the disease-free equilibrium ε is locally asymptotically stable since 1; R < meaning ZIKV infection would be eradicated from the population. The computational results of the study revealed that combining the two interventions of vaccination and treatment concomitantly proffers an optimal control strategy in taming the transmission of the virus than a single intervention strategy.
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