Dynamic analysis of mathematical model of the spread of yellow virus in red chili plants through insect vectors with logistical functions

Abstract

Plant cultivation in the tropics can make it easier for farmers to determine when the planting season is good, with the hope of satisfying production. Unfortunately, the changing seasons at this time are irregular. The low productivity is caused by various things, one of which is the occurrence of plant diseases caused by pathogens and spread through insects. One example is the cultivation of red chili plants. It is common for farmers to suffer losses due to the yellow virus (Geminivirus), which is transmitted through insect vectors. These problems can be analyzed using mathematical models. In this paper, we developed a mathematical model of the spread of the yellow virus in red chili plants with the growth of insects as vector carriers of disease following the logistical function. We will show the value of the basic reproduction number R0 from the model by determining the dominant eigenvalue of the next generation matrix. The results show that when the R0 is smaller than one, non-endemic equilibrium points will be stable. Also, we provide examples of numerical simulations that describe the population of models that have been developed. The simulation results provided show that if the use of V. lecanii is more than 30%, the population of infected plants in the vegetative and generative phases will experience extinction, as will the infected population of B. tabaci.