Fractional-order model for myxomatosis transmission dynamics: Significance of contact, vector control and culling

Abstract

A fractional-order model for myxomatosis transmission dynamics is developed and analyzed. The presented compartmentalized model is based on the Caputo-Fabrizio fractional-order type owing to its flexibility when handling initial value problems. The model properties such as positivity and boundedness are proved using a one-parameter Mittag-Leffler function approximation. The model reproduction number, \scrR 0, is determined using the next-generation method assuming the integer-order case of the model and is used to determine the conditions for disease progression as well as its containment. Furthermore, the existence and uniqueness of nontrivial solutions of the model are shown using the fixed point theory. In addition, we performed sensitivity analysis of model parameters as inputs with \scrR 0 as the output using the Latin hypercube sampling (LHS) scheme and determined the key processes that must be targeted in order to contain the infection. The significance of parameter values was based on p-values obtained after performing Fisher-transformation on the obtained partial rank correlation coefficients. More still, pairwise comparison of significant parameters was carried out with and without false discovery rate adjustment to ensure that significantly different processes are not falsely disqualified. Our results show that the model has a locally asymptotically stable disease-free equilibrium when \scrR 0 is less than one and a unique endemic equilibrium whenever \scrR 0 is greater than one. The sensitivity analysis process revealed that on one hand, the processes described by parameters related to contact have the greatest potential of making the epidemic worse if not curtailed. On the other hand, the processes associated with recovery of rabbits are highly vital in containing the disease when enhanced. Although the obtained median of the reproduction number is around 1, we observe that while there are combinations of parameters that can make the infection worse, there are also combinations that can be enhanced to curtail the infection. We further observed that increased memory/dependence of future values of the model on previous states predicts lower peak values of infected cases in the short-term but higher equilibrium values in the long-term. Based on our results, we recommend that infected rabbits be isolated to reduce contact with uninfected ones. Furthermore, efforts must be put in place to minimize the contact between the vectors and rabbits as well as reduce the vector population if the disease is to be contained. In the worst-case scenario, culling of infected rabbits can be applied to reduce the likelihood of transmission through contact between susceptible and infected rabbits.