Role of cross-border mobility on the backward bifurcation of malaria transmission model: Implications for malaria control in Nepal

The existence of backward bifurcation indicates an obstacle to disease eradication even when the basic reproduction number falls below unity. Bifurcation analysis allows us to identify causes for backward bifurcation, thereby helping to design a strategy to avoid such phenomena for disease eradication. In this study, we perform an in-depth bifurcation analysis of a malaria model incorporating cross-border mobility between two countries to explore mobility’s role in backward bifurcation. Our analysis reveals that cross-border mobility can be a primary driving force for backward bifurcation in malaria dynamics. This novel result with cross-border mobility bringing backward bifurcation advances the traditional idea of disease-induced death being the primary driver of backward bifurcation. Using the malaria case in Nepal with cross-border mobility between Nepal–India, we validated analytical results by numerical simulations. Our model predicts that the disease-free equilibrium exists only if cross-border mobility or infection abroad are absent and malaria eradication is possible in Nepal. Otherwise, there is the coexistence of three endemic equilibria with a lower and higher stable epidemic level. Results on the bifurcation of our model may be helpful to control dynamics in order to maintain the malaria epidemic at a low level if it cannot be eradicated due to the entry of cases through cross-border mobility.