Mathematical Modeling of the Transmission Dynamics of Fowl Pox in Poultry

In this study, researchers present two models that examine the transmission dynamics of fowl pox among birds based on the mode of transmission of the disease in poultry. Using methods from dynamical systems theory equilibrium analysis of the first model showed that the disease free equilibrium is stable if α N <(d1+μ+r1), β<γ. The endemic equilibrium is asymptotically stable if β-γ<α (d1+μ+r1)/k. That is, fowl pox will not invade the poultry if the rate at which the susceptible birds (β) are introduced into the poultry is greater than the rate at which the susceptible birds become exposed to infection (γ). It was also established that R0<1 if S0>Sc where Sc = (d1+μ+r1)/α and R0 = γ S0/(d1+μ+r1). The second model is stable if the rate at which the infected birds recover and the rate at which mosquitoes die are high. Also if the growth rate of mosquito is less than the death rate of mosquito.