Mathematical Analysis of a Vaccination–Culling Model for the Control of Fowl Pox in Birds

Abstract

Fowl pox is a highly contagious viral disease that poses significant economic challenges to poultry production through reduced productivity, morbidity, and mortality. This study extends an existing fowl pox transmission model by incorporating vaccination of susceptible and newly recruited birds, culling of symptomatic infectious birds, and separate symptomatic and asymptomatic infectious classes to better capture disease progression and control dynamics. A deterministic compartmental model consisting of susceptible, exposed, symptomatic infectious, asymptomatic infectious, and recovered bird populations is formulated and analyzed. Fundamental properties of the model, including positivity and boundedness of solutions, are established. The disease-free equilibrium and the basic reproduction number are derived using the next-generation matrix approach. Using biologically relevant parameter values, the basic reproduction number was evaluated as , indicating that each infectious bird generates less than one secondary infection on average. Theoretical analysis shows that the disease-free equilibrium is both locally and globally asymptotically stable whenever . Sensitivity analysis reveals that the culling rate and vaccination rate exert the strongest negative influence on disease transmission, with sensitivity indices of and , respectively, while the symptomatic transmission coefficient and recruitment rate contribute most positively to disease spread. Numerical simulations demonstrate that increasing vaccination coverage and culling rates substantially reduce the exposed, symptomatic, and asymptomatic infectious bird populations while increasing the recovered population. The results indicate that the combined implementation of vaccination and culling is an effective strategy for suppressing fowl pox transmission and preventing disease persistence in poultry populations. These findings provide quantitative support for the adoption of integrated vaccination and culling programmes in poultry farms and contribute to the mathematical understanding of fowl pox control.