Spillover Modelling and Dynamics in Multi-Host Pathogens Transmission

Abstract

Many pathogens of concern to both human and animal populations exhibit a generalist nature of infecting multiple host species. The behavior and transmission dynamics within reservoir hosts not only influence outbreaks within their own population but also contribute to the spillover of pathogens to new target hosts. Although existing works have incorporated spillover transmission into zoonotic models, significant gaps remain in understanding the epidemic or endemic spread of disease in target hosts due to spillover, particularly in epizootic contexts. One typical example is the monkeypox. In this research, by delineating host roles and examining transmission dynamics of monkeypox, we can effectively assess the risk of spillover events and inform mitigation and control strategies. We start with a foundational framework that models monkeypox transmission in a single host species. Two kinds of stochasticity, namely demographic and environmental stochasticity, are incorporated. We find population-size-dependent shift in the relative influence of demographic and environmental stochasticity on disease dynamics. By developing a basic reservoir-target epidemic systems, we observe that the basic reproduction number of the system fails to capture interspecific transmissibility. Our novel threshold derived from the final size relation reflects the influence of spillover processes and intraspecific transmission within target hosts, providing an appropriate measure for quantifying the spillover phenomena. Subsequently, incorporating population demographics allows us to determine the population extinction threshold and the maximum persistence threshold. We further verify that stochasticity in the spillover rate induces Phenomenological bifurcation (P-bifurcation) within the model. These analyses reveal that the spillover rate is the most critical factor influencing the epidemic and endemic prevalence in target hosts. Finally, we evaluate the effectiveness of reservoir control strategies such as quarantine and culling. Our findings indicate that the interactions between spillover events and the implementation of reservoir control strategies lead to complex dynamics due to the higher codimension bifurcations. A novel observation from our analysis and numerical simulations is the existence and collision of two limit cycles generated by distinct endemic equilibria within the system. Our study underscores the importance of controlling spillover events and managing reservoir prevalence as key interventions to mitigate spillover effects on target hosts.