Transmission dynamics and control of Gnathostomiasis:Insights from dynamics modelling and Optimal control.

Abstract

Gnathostomiasis is a system food-borne parasitic disease. Gnathostomiasis is usually consumed/ingested in contaminated raw fish, which is one of the main risk factors. The parasite can infect many animals including domestic and wild felines and canines, domestic and wild pigs. Despite the fact that the disease is common in several regions of Asia and South America, very few patients have been reported in Africa. Control strategies including disinfecting contaminated water sources, providing medical care and reducing contact rate have been introduced to reduce Gnathostomiaisis disease. In this thesis, a Gnathostomiasis model was developed and analyzed. Positivity and boundedness of solutions were explored, and computed basic reproduction number (R0) using the method of the next generation. R0 was used to find out the disease-free equilibrium’s local stability along with the endemic equilibrium’s existence. We found out that endemic equilibrium is unique for R0 > 1 and the disease-free equilibrium is globally asymptotically stable when R0 < 1. Sensitivity analysis and numerical results were obtained. We observed that the processes related to contact of individuals to Gnathostoma infected environments, water sources or food have the potential of worsening the disease when increased. In addition, increased shedding of the pathogen into the environment also has the potential of increasing the disease burden. We also extended our force of infection (λ), that is adding the force of infection for consuming food contaminated with the pathogen. We only focused on the numerical simulation for the extended force of infection (λ), considering the contribution of eating contaminated food. Our results showed a higher estimation of the number of infections and hence the disease burden. The model was improved to consider controls that target the reduction in the number of infections. We found that all controls should be implemented to contain the infection. For the optimal control model, we introduced three controls, and implemented objective cost function to reduce the infected population and accompanying costs. We solved the numerical optimal control problem using the forward and backward sweep method. From the numerical results, we deduced that when all the controls are implemented, the disease can be contained