School of Mathematics and Statistics, The University of Melbourne, Parkville, Australia.
Department of Mathematics, Bangabandhu Sheikh Mujibur Rahman Science and Technology University, Gopalganj, 8100, Bangladesh.
Bull Math Biol. 2022 Jul 1;84(8):81. doi: 10.1007/s11538-022-01036-0.
Malaria is caused by Plasmodium parasites which are transmitted to humans by the bite of an infected Anopheles mosquito. Plasmodium vivax is distinct from other malaria species in its ability to remain dormant in the liver (as hypnozoites) and activate later to cause further infections (referred to as relapses). Mathematical models to describe the transmission dynamics of P. vivax have been developed, but most of them fail to capture realistic dynamics of hypnozoites. Models that do capture the complexity tend to involve many governing equations, making them difficult to extend to incorporate other important factors for P. vivax, such as treatment status, age and pregnancy. In this paper, we have developed a multiscale model (a system of integro-differential equations) that involves a minimal set of equations at the population scale, with an embedded within-host model that can capture the dynamics of the hypnozoite reservoir. In this way, we can gain key insights into dynamics of P. vivax transmission with a minimum number of equations at the population scale, making this framework readily scalable to incorporate more complexity. We performed a sensitivity analysis of our multiscale model over key parameters and found that prevalence of P. vivax blood-stage infection increases with both bite rate and number of mosquitoes but decreases with hypnozoite death rate. Since our mathematical model captures the complex dynamics of P. vivax and the hypnozoite reservoir, it has the potential to become a key tool to inform elimination strategies for P. vivax.
疟疾是由疟原虫引起的，疟原虫通过受感染的按蚊叮咬传播给人类。间日疟原虫与其他疟原虫不同，它能够在肝脏中休眠（作为休眠体），然后在以后激活，导致进一步的感染（称为复发）。已经开发出描述间日疟原虫传播动力学的数学模型，但大多数模型都无法捕捉休眠体的真实动态。那些能够捕捉到复杂性的模型往往涉及到许多控制方程，使得它们难以扩展以纳入间日疟原虫的其他重要因素，如治疗状况、年龄和妊娠。在本文中，我们开发了一个多尺度模型（一个积分微分方程组系统），该模型在种群尺度上涉及到一组最少的方程，同时嵌入了一个能够捕捉休眠体库动态的宿主内模型。通过这种方式，我们可以用种群尺度上最少的方程来获得间日疟原虫传播动力学的关键见解，从而使这个框架很容易扩展以纳入更多的复杂性。我们对我们的多尺度模型进行了关键参数的敏感性分析，发现间日疟原虫血期感染的流行率随着叮咬率和蚊子数量的增加而增加，但随着休眠体死亡率的增加而降低。由于我们的数学模型捕捉到了间日疟原虫和休眠体库的复杂动态，它有可能成为间日疟原虫消除策略的重要工具。
