A Multi-level Model for a Vector-Borne Organ to Tissue life Cycle Dynamics

Abstract

Introduction: Malaria is among the World’s most lethal infectious disease. It is caused by a parasitic pathogen transmitted by the Anopheles mosquito, which inoculates sporozoites into the human host during a blood meal. The population dynamics of malaria are well-known for their complexity, stemming not only from the parasite’s lifecycle, which involves two hosts (humans and mosquitoes)but also from the intricate replication and transmission cycles across different levels of the infectious disease system organization. Like other infectious disease systems, malaria infections inherit multilevel and multiscale systems, which pose significant challenges to efforts aimed at eliminating and ultimately eradicating the infection in a malaria-endemic population. Methodology Mathematical modeling in the study of complex system has proven to be an invaluable tool for understanding and predicting the behaviour and dynamics of a complex system within the domain of complexity science. Thus, in this study, we propose a multiscale modelling framework that captures the dynamics of malaria across three organizational levels within infectious disease systems implicated in the spread of malaria in a community. We begin by formulating a mathematical model to describe the development and progression of malaria parasites within the liver and tissue(blood) stages of an infected human host. This is followed by the formulation of a multiscale model that integrates both the inside(i.e.,the organ-tissue level)host and the outside (i.e., the host level) host malaria dynamics. Results Mathematical analysis for both the malaria models presented in this study was carried out and proved that all the models are mathematically and epidemiologically well-posed. We also compute the basic reproduction number R0 for both models and use the R0 to determine the local and global stability of the disease-free equilibriumas well as the local stability of endemic equilibrium of both models, respectively. We demonstrate that if R0 < 1, then the diseasefree equilibrium pointy of both models is locally and globally asymptotically stable, respevctively. However, if R0 > 1 the endemic equilibrium point of both models is locally asymptotically stable. The numerical results for both the models have demonstrated that the goal of intervention during malaria infection should be to reduce the rates at which merozoites and gametocytes invade healthy liver tissue as well as the blood cells. Hence it is recommended that interventions during malaria infection be directed on reducing the pace at which merozoites infect healthy blood cells and the density of merozoites in circulation. Conclusion The study presents a method that incoporates the complexity of malaria pathogens which is significant not only for malaria treatment but also for other vector-borne disease system control treatment strategies.