Bifurcation Analysis of Model for the Effect of Vaccination on the Transmission Dynamics of Rotavirus Disease

Hellen Namawejje, Livingstone S. Luboobi, Dmitry Kuznetsov, Eric Wobudeya

Abstract


In this work, we investigated the effect of vaccination on the transmission dynamics of rotavirus disease. Rotavirus can be spread both through direct or indirect transmission contact with infected children or unhygienic environment. Vaccination is administered in three doses. We determined both the disease free equilibrium point, P0, and the endemic equilibrium point, P∗ kV. The disease-free equilibrium point, P0, is both locally and globally asymptotically stable if the effective reproduction number RV < 1 and unstable if RV > 1. The endemic equilibrium point, P∗ kV, for k = 0,1,2,3 with vaccination exists if and only if RV > 1. In case of no vaccination, the endemic equilibrium point, P∗ 0V, has a unique stable endemic equilibrium point whenever the basic reproduction number without vaccination R0V > 1 and a backward bifurcation exists. Numerical results show that vaccination reduces the degree of susceptibility and infectiousness when children are exposed to the disease. Hence help to reduce rotavirus disease among children.

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