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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 &lt;1, the disease free equilibrium E0 is globally asymptotically stable, meaning that the malaria disease will eventually die out; and if R 0 &gt;1, E 0 becomes unstable. When R 0 &gt;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 &gt;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.

On latencies in malaria infections and their impact on the disease dynamics