Dynamics of a two-group structured malaria transmission model

Abstract

Malaria is an infectious vector-borne disease of global public concern, with high morbidity and mortality in children less than 5 years old. We propose a two-group malaria model structured by age with the SEISdynamic in individuals aged below 5 years old, and SEIRSdynamic in individuals aged above 5 years. We compute the basic reproduction number and show that the DFE is locally asymptotically stable when R01, we prove the existence of a unique endemic equilibrium. On the other hand, if R0≤1, under certain conditions, the system can have one endemic equilibrium or two endemic equilibria. Using partial rank correlation coefficients and Latin hypercube sampling, sensitivity analysis is carried out to determine the relative importance of model parameters to disease transmission. The average per capita biting rate of mosquitoes on susceptible humans under 5 years old b2, recovery rate of infectious humans under 5 years old ωe, recovery rate of infectious humans over 5 years old ωaand the recruitment of mosquitoes Λvare the most impactful parameters. Graphically, it is shown that any intervention to reduce the contact between the mosquito and individuals under five has a greater positive impact on the level of endemicity in the total population compared to the case when the contact between mosquitoes and individuals over 5 years old is reduced. The public health implication of this result is that the fight against malaria should be stepped up in children under 5 years old to mitigate its spread.

Keywords

• Age-structured
• Malaria
• Basic reproduction number
• Local stability
• Sensitivity analysis