On the Delayed Ross–Macdonald Model for Malaria Transmission

Abstract

The feedback dynamics from mosquito to human and back to mosquito involve considerable time delays due to the incubation periods of the parasites. In this paper, taking explicit account of the incubation periods of parasites within the human and the mosquito, we first propose a delayed RossMacdonald model. Then we calculate the basic reproduction number R 0 and carry out some sensitivity analysis of R 0 on the incubation periods, that is, to study the effect of time delays on the basic reproduction number. It is shown that the basic reproduction number is a decreasing function of both time delays. Thus, prolonging the incubation periods in either humans or mosquitos (via medicine or control measures) could reduce the prevalence of infection.

Parameterization and Sensitivity Analysis of a Complex Simulation Model for Mosquito Population Dynamics, Dengue Transmission, and Their Control

“…These results are consistent with other modeling studies reporting the importance of mosquito survival or mortality, [14][15][16][17][18][19][20][21] biting rate, 6,14,15,17,18,22 and length of the infectious period in the host 6,14,21,[23][24][25][26][27] in determining the dynamics of mosquitoborne diseases. However, our results go one step further by identifying specific causes of mosquito mortality and the aspects of biting behaviors that may be most influential.…”

“…Unlike some other studies, 14,19,48 we did not identify parameters associated with the extrinsic incubation period (EIP) in the mosquito as being important. This may be a function of how the processes determining the EIP are incorporated into the model and not because it is unimportant.…”

Analysis of a Vector-Bias Model on Malaria Transmission

“…In order to prove that the disease-free steady state is stable if and only if R τ 0 < 1, we consider the properties of the function F and follows the steps of proof by Ruan et al (2008) and Wei et al (2008). The function F is analytic with F (0, τ ) = η(μ + ν)(1 − R τ 0 ) and F (λ, 0) = λ 2 + (μ + ν + η)λ + η(μ + ν) − βαq p l .…”

Malaria dynamics with long latent period in hosts

“…Moreover, under additional conditions, all admissible positive solutions converge to the unique endemic equilibrium. They have generalized the conclusion of Ruan et al [60] that longer incubation periods lead to lower prevalence of the infection, regardless of the specific form of the distributions.…”

“…The incubation period was incorporated first by Sharpe and Lotka [63] as a discrete time delay. The delayed Ross-Macdonald model was later modified and analyzed in [3,37,60]. It was concluded that prolonging the incubation periods reduces the prevalence of the disease.…”