Controlling transmission of infectious diseases in spatially structured populations by culling, vaccination and non-pharmaceutical interventions: Pair approximation models

This thesis demonstrated the value of pair approximation models in (i) describing spatial transmission and strategic control of foot and mouth disease (FMD) by vaccination and culling in view of the situations in endemic or near-endemic countries and (ii) exploring impacts of adoption of non-pharmaceutical interventions (NPIs) resulting from interactions between spatially connected individuals, on the spread of a general infection. Factors relevant to the dynamics of FMD in endemic or near-endemic and often low-income countries that we considered are frequent disease re-introduction, long-term waning of natural immunity, vaccine waning and constrained culling and vaccination. To minimize the impact of disease re-importation, vaccine waning and natural immunity waning on the dynamics of FMD by a limited supply of vaccines or vaccination resources, it is ideal to combine rapid deployment of ring vaccination in farms neighboring infected premises, with spread-out deployment of prophylactic vaccination during disease-free phases, such that supplies last as long as possible. The advantage of rapid culling in farms neighboring confirmed FMD source infections (direct contact or DC culling) over culling in infected premises (IP culling) only is that the former removes a population of farms that would otherwise provide ground for infection and further transmission of the disease. However, the optimal strategy for controlling FMD by culling is prompt diagnosis and rapid deployment of IP culling and DC culling. Secondly, this thesis explored the interaction between spatial transmission of an infection and the spread of adoption of NPIs, which is stimulated by being neighbors of infected individuals (exposure learning) or individuals who practice NPIs (social learning). A newly introduced infection is likely to die out without developing into an epidemic if the neighborhood of the source infection is made up of individuals who can avoid infection and further disease transmission through the practice of strict NPIs at all times. If adoption of NPIs begins to take place during an outbreak, then exposure learning followed by prompt adoption of strict NPIs and avoidance of infection from the infectious neighbors, is more effective than social learning. However, social learning can outperform exposure learning if the former begins well in advance of the infection outbreak. Contrary to commonly observed phenomena, increasing the initial source infections, who are surrounded by individuals who exercise strict NPIs, can decrease the infection peak. We conclude that (i) in order to attain global eradication of FMD, more spatially oriented mathematical models tailored to countries that are still endemic or near-endemic should be developed and (ii) more spatially oriented models that explore effects of NPIs on the regulation of infectious diseases should be developed.