title: On latencies in malaria infections and their impact on the disease dynamics.
abstract: In this paper, we modify the classic Ross-Macdonald model for malaria disease dynamics by incorporating latencies both for human beings and female mosquitoes. One novelty of our model is that we introduce two general probability functions (P 1 (t) and P 2 (t)) to reflect the fact that the latencies differ from individuals to individuals. We justify the well-posedness of the new model, identify the basic reproduction number R0 for the model and analyze the dynamics of the model. We show that when R 0 <1, the disease free equilibrium E0 is globally asymptotically stable, meaning that the malaria disease will eventually die out; and if R 0 >1, E 0 becomes unstable. When R 0 >1, we consider two specific forms for P 1 (t) and P 2 (t): (i) P 1 (t) and P 2 (t) are both exponential functions; (ii) P 1 (t) and P 2 (t) are both step functions. For (i), the model reduces to an ODE system, and for (ii), the long term disease dynamics are governed by a DDE system. In both cases, we are able to show that when R 0 >1 then the disease will persist; moreover if there is no recovery (γ1=0), then all admissible positive solutions will converge to the unique endemic equilibrium. A significant impact of the latencies is that they reduce the basic reproduction number, regardless of the forms of the distributions.
authors: Department of Applied Mathematics, University of Western Ontario, London, Ontario, N6A 5B7, Canada. yxiao26@uwo.ca
authors: Yanyu
authors: Y
authors: Xiao
authors: Xingfu
authors: X
authors: Zou
mesh_terms: D000818:Animals; D003198:Computer Simulation; D009033:Culicidae / Q000469:parasitology*; D006801:Humans; D008288:Malaria / Q000453:epidemiology* / Q000469:parasitology*; D015233:Models, Statistical; D010961:Plasmodium / Q000472:pathogenicity*; D013997:Time Factors