| dc.description.abstract | Fowlpox disease poses a real threat to domestic birds, especially the chicken and turkeys in Uganda and the world, despite the tremendous efforts put in place to avert the transmission. The disease prevalence varies depending on climate change, vector dynamics, vaccination, good management, and hygienic practices. This is primarily due to seasonal variations that affect mosquito population and fowlpox virus concentration in the environment. However, the effects of seasonality on disease dynamics are not fully understood. Therefore, a deterministic mathematical model is formulated and used to determine the impact of seasonality. In addition, the stochastic model derived from the deterministic model was developed and used to estimate the probability of fowlpox disease outbreak, and optimal control strategies for disease extinction was explored. The next generation method was used to compute the basic reproduction number $\Re_{0}$. The model exhibits backward bifurcation when $\Re_{0}<1$, which indicates the persistence of the disease in poultry birds. However, for $\Re_{0}>1$, a Continuous-Time Markov Chain (CTMC) was formulated and used to determine the probability of disease outbreak. Results showed that the probability of disease extinction increases when infected mosquitoes introduce the infection, and the probability of disease outbreak increases with infection originating from infected chicken and the concentration of the virus in the environment. Results also showed that host-vector and environmental transmission routes have a high probability of disease outbreaks. The results also showed that time-average approach overestimates the disease risk and underestimates the disease risk as the amplitude of the mosquito seasonal oscillation was varied from 0.3 to 0.8. In addition, results show that with the linear operator approach, $\Re_{0}<1$ when fowlpox virus decay rate, $\eta$ is varied. In addition, results demonstrated that environmental decontamination yields better control results than insecticide spraying, though the measure does not eliminate fowl pox disease in chicken. On the other hand, the application of both control measures produces much better results. | en_US |
