Abstract
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.
Highlights
Gonorrhea is a major public health challenge today, due to the high incidence of infections accompanied by a dwindling number of treatment options (Schiffert Health Center, 2011)
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
The basic reproduction numbers for the cases were computed with the graphs
Summary
Gonorrhea is a major public health challenge today, due to the high incidence of infections accompanied by a dwindling number of treatment options (Schiffert Health Center, 2011). Y. in 1976, where they took into consideration the fact that; the spread of gonorrhea in a population is nonuniform, and by partitioning the population into n groups they developed a deterministic model for Gonorrhea in a non-homogenous population They carried out a study of the asymptotic stability properties of the model, to show that the disease will die out either for all positive initial disease levels or for none, depending on the contact rates and the lengths of infectious periods. In reality, treated individuals acquire susceptible status to move to susceptible compartment or die naturally, its only after interacting with an infectious individual that a treated individual becomes exposed since recovery from gonorrhea does not confer permanent immunity Incorporating this term in the model equations is not correct. K., et al, 2016, and developed a more realistic model that addresses the issues raised, by incorporating natural immunity effects into the dynamics of neisseria gonorrhea infection
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