Abstract:
Foot and Mouth disease (FMD) remains a global concern despite that many developed
countries have eliminated it. This is because FMD is still endemic in some parts of the world,and it can spread around the world via several transmission routes including international trade of affected agricultural products. Botswana which experiences recurring outbreaks of FMD in some parts of the country, FMD has a major negative impact on the beef industry as its outbreaks prevent the country from gaining access to major markets such as the Europian Union (EU). Hence, there is a need to eliminate the disease to prevent its spread, future outbreaks and to increase control measures. In this thesis, two mathematical models for the dynamics of FMD accounting for the direct, indirect and spatial transmission are formulated and analysed. The first model is a homogeneous-mixing model of FMD with carriers. We derived the basic reproduction number, R0, and analysed the existence and stability of the disease-free equilibrium. The parameters used in our model were estimated from literature and sensitivity analysis of selected parameters on R0 as well as the full model was performed using the Latin Hypercube Sampling scheme (LHS). The sensitivity analysis results show that the parameters β1 and β2, which represent direct and indirect transmission of the virus from the infected animals and environment, respectively, together with the shedding of the virus into the environment by the infected animals, have the greatest positive Partial Rank Correlation Coefficients (PRCCs) whilst the parameter for the recovery rate of the infected (α) and the increase in carrier animals (γ) have the highest negative PRCCs. If the processes described by parameters with negative PRCCs are increased, then chances of containing the FMD infections are enhanced. Our numerical simulations show that reducing the contact between susceptible animals and infected surfaces by 80% can reduce the disease burden by up to 71%. However, a combination of controls including reducing contact with infected surfaces and disinfecting leading to increased decay of the pathogen by 100 folds from the baseline value can lead to elimination of the disease. Our second model is a pair approximation model of FMD with carriers. The results show that both the symptomatic and asymptomatic (carriers) nodes in a network have the potential to aggravate spread the disease. The results also show that R0 is proportional to the infection rate from the carriers associated with lower recovery rates in a network. Therefore, early identifications of infected animals and their contacts in the initial stages of an outbreak followed by prompt application of spatially-oriented control measures, can help contain the disease. We recommend that, when controlling the disease, a combination of control measures be implemented if the disease is to be contained in a shorter period of time. We further
suggest that cost-effectiveness analysis and optimal control of admissible controls be studied to ascertain the best combination of disease containment measures.
