A Model for the Coevolution of Immunity and Immune Evasion in Vector‐Borne Diseases with Implications for the Epidemiology of Malaria

Abstract

We describe a model of host-parasite coevolution, where the interaction depends on the investments by the host in its immune response and by the parasite in its ability to suppress (or evade) its host's immune response. We base our model on the interaction between malaria parasites and their mosquito hosts and thus describe the epidemiological dynamics with the Macdonald-Ross equation of malaria epidemiology. The qualitative predictions of the model are most sensitive to the cost of the immune response and to the intensity of transmission. If transmission is weak or the cost of immunity is low, the system evolves to a coevolutionarily stable equilibrium at intermediate levels of investment (and, generally, at a low frequency of resistance). At a higher cost of immunity and as transmission intensifies, the system is not evolutionarily stable but rather cycles around intermediate levels of investment. At more intense transmission, neither host nor parasite invests any resources in dominating its partner so that no resistance is observed in the population. These results may help to explain the lack of encapsulated malaria parasites generally observed in natural populations of mosquito vectors, despite strong selection pressure for resistance in areas of very intense transmission.

Transmission dynamics and underreporting of Kala-azar in the Indian state of Bihar

“…-----There are plenty of studies of the dynamics of vector-borne diseases using mathematical models (e.g., Dengue [22]; Malaria [28]; West Nile virus [49]). The only mathematical study of the dynamics of AVL (Kala-azar) appears to be that of Dye and Wolpert in 1988 [21].…”

“…The variability in the infectious period, intrinsic and extrinsic incubation/latent periods, is in the distributions for m 1 , n 1 and n 2 , respectively. Discrete (integer value) uniform distributions are chosen for m 1 , n 1 and n 2 with estimated ranges in the intervals [1,3], [4,28] and [11,39], respectively (see references in Table 2 and references [1,3,4,7,29,36]). …”

On the Delayed Ross–Macdonald Model for Malaria Transmission

“…Subsequent contributions have been made to extend the Ross-Macdonald malaria models considering age structure in the human population (Aron and May, 1982;Dietz, 1988;Anderson and May, 1991), acquired immunity (Aron and May, 1982;Aron, 1988), latency (Koella, 1991;Lopez et al, 2002;Koella and Antia, 2003;Koella and Boëte, 2003), spatial heterogeneity (Dye and Hasibeder, 1986;Hasibeder and Dye, 1988;Gupta and Hill, 1995;Gupta et al, 1994;Torres-Sorando and Rodriguez, 1997;Rodriguez and Torres-Sorando, 2001), individual-based models , habitat-based models (Gu and Novak, 2005), integrated models (McKenzie and Bossert, 2005), among other aspects (Bailey, 1982;Chitnis et al, 2006;Gu et al, 2003b;Killeen et al, 2000;McKenzie, 2000;Ngwa, 2006;Smith et al, , 2005.…”

Mathematical models of the Spread of Malaria with the vertical transmission (congenital malaria)

“…Anderson and May [1], Aron and May [3], Koella [18] and Nedelman [27] have written some good reviews on the mathematical modeling of malaria. Some recent papers have also included environmental effects ( [22,45] and [46]) the spread of resistance to drugs ( [4] and [19]), and the evolution of immunity [20]. Recently, Ngwa and Shu [29] and Ngwa [28] proposed an ordinary differential equation (ODE) compartmental model for the spread of malaria involving variable human and mosquito populations, with a susceptible-exposedinfectious-recovered-susceptible (SEIRS) pattern for humans and a susceptible-exposed-infectious (SEI) pattern for mosquitoes, greatly developed the mathematical models of malaria, but the vertical transmission between human has not been studied.…”