Modelling the effects of virus-resistant planting material on the transmission dynamics of banana bunchy top disease

Abstract

Banana bunchy top disease (BBTD) significantly threatens banana production, considerably endangering food safety and security. Aphid vectors and the use of latently infected planting materials disseminate the disease. This paper uses a deterministic mathematical model to examine the BBTD dynamics while considering the Banana Bunchy Top Virus (BBTV)-resistance of the planting material. After model formulation, we establish the positivity and boundedness of the model solution. We derived the effective reproduction number via the next-generation matrix approach and used it to investigate the asymptotic stability of the model equilibrium points using the Lyapunov function. To support the stability results, we conducted a bifurcation analysis. The bifurcation analysis confirmed a forward bifurcation, implying that the disease-free equilibrium point is stable when the effective reproduction number is less than one and unstable when the effective reproduction number is greater than one. The endemic equilibrium point is also stable when the effective reproduction number is greater than one and unstable otherwise. Finally, we apply the fourth-order Runge-Kutta method to simulate the proposed model. One limitation of our research is the need for real data to support our findings. in this instance, we used simulated data from earlier studies to conduct numerical simulations in this study. The results revealed that replanting with BBTV-resistance planting material while the rate of removing symptomatic infected plants is [Formula: see text] reduces the number of latent and symptomatic infected banana plants by [Formula: see text] and [Formula: see text], respectively, in two years. Moreover, it was observed that increasing the rate of roguing to [Formula: see text] and replanting with BBTV-resistant planting material remaining at [Formula: see text] cleared the diseased plants in 10 months. Hence, it eliminates the disease. Therefore, the numerical simulation results suggest that while virus-resistant planting materials alone can reduce disease prevalence, they are most effective when combined with a timely roguing strategy. The results indicate that increasing the number of resistant plants beyond a certain threshold can lead to disease elimination. It is recommended that scientists provide farmers with reliable BBTV-resistant planting material and farming education on the safe way to rogue infected plants and replant.

Keywords: BBTD; BBTV; Banana bunchy top disease; Bifurcation analysis; Mathematical modeling; Planting material; Transmission dynamics; Virus resistant.

Fig. 1

Compartmental diagram illustrating the dynamics of BBTD, considering banana plants’ resistance to BBTV infection. The green rectangles denote susceptible banana plants and aphid vectors, whereas red rectangles signify symptomatic infected banana plants and contaminated aphid vectors. The blue rectangle represents latently infected banana plants. The solid lines indicate transitions between compartments, recruitment rates, harvesting rates, and vector mortality rates. The dashed lines illustrate the typical interactions between several compartments in transmitting the disease.

Fig. 2

Sensitivity indices of the model parameters.

Fig. 3

The forward bifurcation diagram for the banana bunchy top transmission dynamics model with resistant planting material. When , the disease-free equilibrium is stable. However, when , the disease-free equilibrium is unstable, while the endemic equilibrium is stable. The parameter values in Table 2 with the initial condition and were employed for the simulation.

Fig. 4

The impact of resistance breed () on the number of susceptible banana plants () on the farm when no other control strategy applied and , , .

Fig. 5

The impact of resistance breed () on the number of latent infected banana plants () in the farm when no other control strategy applied and , , .

Fig. 6

The impact of resistance breed () on the number of symptomatic infected banana plants () in the farm when no other control strategy applied and , , .

Fig. 7

The impact of resistance breed () on the number of symptomatic infected banana plants () on the farm when no other control strategy was applied and , , .

Fig. 8

The impact of resistance breed () on the number of symptomatic infected banana plants () on the farm when no other control strategy was applied and , , .

Fig. 9

Banana population dynamics when and .

Fig. 10

Banana population dynamics when and .