| dc.identifier.citation | : Jimrise O. Ochwach, Mark O. Okongo, Moses M. Muraya (2021) Mathematical Modeling of Host - Pest Interactions in Stage-Structured Populations: A Case of False Codling Moth [Thaumatotibia leucotreta. Journal of Progressive Research in Mathematics, 18(4), 1-21. Retrieved from http://scitecresearch.com/journals/index.php/jprm/article/view/2087 and employment in many countries (Blomefield et al., 1989; Gillaga et al., 2011). FCM is widely distributed across Africa and has been reported in over 40 Africa countries , including Kenya (Venette et al., 2003; Stibick. 2008). The FCM is not considered to be established outside of Africa (Venette et al., 2003). However, it is commonly intercepted during quarantine inspections in Europe and United States (Gianni et al., 2014). Consignments of roses from Kenya to Europe have been intercepted in recent years due to the presence of FCM. When a single living individual of FCM is found within a consignment at any stage of development, the entire consignment is rejected (FPEAK, 2021). This is because FCM is on the European Commission’s (EC) list of harmful organisms that should be regulated as quarantine pests to prevent its introduction into Europe, where it could harm a variety of outdoor and greenhouse crops (Moore, 2012; Mkiga et al., 2019). Therefore, FCM is a pest of phytosanitary concern and it impedes export in most international markets, as it is endemic to sub-Saharan Africa (Hofmeyr et al., 1998; Moore, 2012 ). False codling moth is now a quarantine pest on all crops according European Union (EU) plant health (phytosanitary) regulations (EU 2016/2031). Special measures have been introduced for crops that are a known pathway into the EU for serious pests that could damage Europe’s agriculture or environment. These measures include stringent new requirements covering the export of roses to prevent the introduction of FCM into the EU (FPEAK, 2021). The number of FCM interceptions on Kenyan roses has been extremely high (36 in 2018, 36 in 2019, and 24 up to June 2020). This high level of interceptions has been attributed to increased inspection levels, which have risen from 5% in 2011 to 10% now. In 2021, a drastic increase to 50% or even 100% checks for roses from Kenya is expected as a result of the numbers observed in the previous three years. By the end of 2020, this will be determined (FPEAK, 2021). Planning efficient and cost-effective FCM control is a real challenge, which explains why most experimental FCM control strategies fail (Anguelove et al ., 2016). This is because certain parameters can be changed to make biological systems unstable or stable, i.e., if their values pass through bifurcation values. (Murray, 2002; Sergio, 2014; Savary, 2006). Therefore, there is need for more scientific studies on FCM interaction with the host for effective management of the pest. The demand for reliable pest infestation models is increasing because they are helpful in defining problems, organizing thoughts, identifying areas to investigate, making predictions, generating hypotheses, and supporting pest management decision-making. They also serve as standard comparisons and offer strategies to improve decision-making on effective pest control (Byers, 1993 & Anguelov et al., 2016). Predicting population dynamics and evaluating pest control scenarios by agro-ecosystem under a variety of environmental conditions can reduce the number and cost of pest control interventions, improving crop yields and quality, as well as health and sustainability (Galilio et al., 2014). Conventional population growth models have been used and modified over time to provide an intuitive foundation for understanding the results of more complex eco-epidemiology modeling (Anderson and May, 1978; Ludwig, 1978; Anderson and May 1979). Recently, these models have been extended to explain the dynamics of human infectious diseases such Malaria, Tuberculosis (TB), Human Immunodeficiency Virus (HIV) and Acquired Immune Deficiency Syndrome (AIDS) and crop diseases (Okongo, 2016). However, very little attention have been given to host- pest interactions particularly in insect pest management. This study attempt to develop the host pest interaction model to simulate stage structure ofFCM interaction with the host. Demographic models with stage structures have been used to describe changes in population abundance over time and across generations. Since population abundance is the major driving force acting on the host plants, this provides an opportunity to interpret the impact of pest populations on both natural and cultivated plants. (Barclay, 2016 & Galilio et al., 2014). Several differential equations have been used to explain empirical data sets for single species pest population fluctuation over time, both in continuous and discrete forms. Ikemoto et al, (2009) developed a mathematical model for caste differentiation in termite colonies via hormonal and pheromonal regulation to aid in the discovery of primer pheromones and inferring their roles in termite caste differentiation. Barclay and Hariotakis, (1991) developed agestructured population dynamic model combining pheromone baited and food baited traps for insect pest control. Similar models of mating disruption and mass trapping were also developed by Byers, (2007). Sterile release models were developed by Anguelove et al, (2012) to control anopheles mosquito and Barclay (2016) to determine the rate of sterile release. However, most of these mathematical models do not address the population dynamics of FCM and its interaction with the host which this study is seeking to address. In this study, a mathematical model of host -FCM interactions is developed and numerically analysed and results presented in graphical form. | en_US |
