A spatial multiscale mathematical model of Plasmodium vivax transmission

• Published in: Journal of mathematical biology 2025-01, Vol.90 (1), p.13, Article 13
• Main Authors: Elgart, Shoshana, Flegg, Mark B, Mehra, Somya, Flegg, Jennifer A
• Format: Article
• Language: English
• Subjects: Animals; Anopheles - parasitology; Computer Simulation; Constraining; Differential equations; Disease control; Disease transmission; Epidemiological Models; Epidemiology; Human motion; Humans; Malaria; Malaria, Vivax - epidemiology; Malaria, Vivax - parasitology; Malaria, Vivax - transmission; Mathematical Concepts; Mathematical models; Metapopulations; Models, Biological; Mosquito Vectors - parasitology; Nonlinear Dynamics; Nonlinear equations; Plasmodium vivax; Plasmodium vivax - physiology; Populations; Scale models; Sine waves; Sporozoites
• ISSN: 0303-6812; 1432-1416; 1432-1416
• DOI: 10.1007/s00285-024-02166-w

The epidemiological behavior of Plasmodium vivax malaria occurs across spatial scales including within-host, population, and metapopulation levels. On the within-host scale, P. vivax sporozoites inoculated in a host may form latent hypnozoites, the activation of which drives secondary infections and accounts for a large proportion of P. vivax illness; on the metapopulation level, the coupled human-vector dynamics characteristic of the population level are further complicated by the migration of human populations across patches with different malaria forces of (re-)infection. To explore the interplay of all three scales in a single two-patch model of Plasmodium vivax dynamics, we construct and study a system of eight integro-differential equations with periodic forcing (arising from the single-frequency sinusoidal movement of a human sub-population). Under the numerically-informed ansatz that the limiting solutions to the system are closely bounded by sinusoidal ones for certain regions of parameter space, we derive a single nonlinear equation from which all approximate limiting solutions may be drawn, and devise necessary and sufficient conditions for the equation to have only a disease-free solution. Our results illustrate the impact of movement on P. vivax transmission and suggest a need to focus vector control efforts on forest mosquito populations. The three-scale model introduced here provides a more comprehensive framework for studying the clinical, behavioral, and geographical factors underlying P. vivax malaria endemicity.