2020/12/30 by Quentin Richard, Richard, Quentin, Marc Choisy +5
Biochemistry, Genetics and Molecular Biology · Medicine · #Analysis of PDEs (math.AP) #Evolution and Genetic Dynamics #FOS: Mathematics #Malaria Research and Control #Mathematical and Theoretical Epidemiology and Ecology Models
paper · pdf · doi:10.48550/arxiv.2012.15147
openalex publication_date 2020/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In contrast to the many theoretical studies on the transmission of\nhuman-mosquitoes malaria infection, few studies have considered a multiple\nstructure model formulations including (i) the chronological age of humans and\nmosquitoes population, (ii) the time since humans and mosquitoes are infected\nand (iii) humans waning immunity (i.e., the progressive loss of protective\nantibodies after recovery). Such structural variables are well documented to be\nfundamental for the transmission of human-mosquitoes malaria infections. Here\nwe formulate an age-structured model accounting for the three structural\nvariables. Using integrated semigroups theory, we first handle the\nwell-posedness of the model proposed. We also investigate the existence of\nmodel's steady-states. A disease-free equilibrium always exists while the\nexistence of endemic equilibria is discussed. We derive the threshold R0 (the\nbasic reproduction number). The expression of the R0 obtained here particularly\nhighlight the effect of above structural variables on key important\nepidemiological traits of the human-vector association. This includes, humans\nand mosquitoes transmission probability and survival rates. Next, we derive a\nnecessary and sufficient condition that implies the bifurcation of an endemic\nequilibrium. In some configuration where the age-structure of the human\npopulation is neglected, we show that, depending on the sign of some constant\nCbif given by the parameters, a bifurcation occurs at R0 = 1 that is either\nforward or backward. In the former case, it means that there exists a (unique)\nendemic equilibrium if and only if R0 > 1. In the latter case, no endemic\nequilibrium exists for R0<< 1 small enough, a unique exists if R0 > 1 while\nmultiple endemic equilibria exist when 0 <<R0 < 1 close enough to 1.\n