Asian Journal of Pure and Applied Mathematics

Zika virus remains a significant public health concern in humanitarian settings, where overcrowding, inadequate sanitation, and limited access to healthcare facilitate disease transmission. Internally displaced persons (IDP) camps are particularly vulnerable because of increased human–vector contact and close interpersonal interactions that enhance both mosquito-borne and sexual transmission. In this study, a deterministic compartmental model is developed to investigate the transmission dynamics of Zika virus in IDP camps. The model incorporates susceptible, exposed, infectious, pregnancy-associated, and recovered human populations together with susceptible, exposed, and infectious mosquito populations, while explicitly accounting for the effects of overcrowding on disease transmission. The model is shown to be mathematically and epidemiologically well posed through rigorous proofs of existence, uniqueness, positivity, and boundedness of solutions. The disease-free equilibrium and the basic reproduction number, R₀, are derived using the next-generation matrix method. Local and global stability analyses establish that the disease-free equilibrium
is globally asymptotically stable whenever R₀ < 1, indicating that the infection is eliminated irrespective of the initial disease burden. The existence and local stability of the endemic equilibrium are established for R₀ > 1, demonstrating the potential for sustained disease persistence when transmission exceeds the epidemic threshold. The analytical results identify mosquito-to-human transmission, sexual transmission, human-to-mosquito transmission, and overcrowding as key determinants of disease spread. Consequently, integrated intervention strategies combining vector control, reduction of overcrowding, personal protection against mosquito bites, and measures that reduce sexual transmission are essential for controlling Zika outbreaks in humanitarian settings. The proposed model provides a rigorous mathematical framework for understanding Zika virus dynamics and offers a useful foundation for future studies incorporating spatial heterogeneity, seasonality, stochastic effects, optimal control, and data-driven parameter estimation.