TY - JOUR

T1 - A superinfection model on malaria transmission

T2 - Analysis on the invasion basic reproduction number

AU - Aldila, Dipo

N1 - Funding Information:
This research is financially supported by the Indonesian RistekBRIN 2021 with PDUPT re-
Publisher Copyright:
© 2021 the author(s).

PY - 2021

Y1 - 2021

N2 - Malaria is one of the many kinds of vector-borne diseases which threaten many developing countries around the world every year. Malaria is caused by more than one type of Plasmodium, which allows a superin-fection between two kinds of Plasmodium in the human body. This article presents a mathematical model that describes the superinfection between Plasmodium Falciparum and Plasmodium Vivax. The model is developed as a system of a nonlinear ordinary differential equation which accommodates several essential factors, such as birth and death rate, infection process, superinfection phenomenon, recovery rate, etc. Mathematical analysis regarding the existence and stability of fixed points is discussed followed by the construction of the respective ”local” basic reproduction numbers and the ”invasion” basic reproduction numbers between Plasmodium. We found that the malaria-free equilibrium point will be locally stable if both local basic reproduction numbers are less than unity. Our results also indicate that although the ”local” basic reproduction number exhibits the existence of a single Plasmodium equilibrium, it is still possible that this equilibrium is not stable if the invasion basic reproduction number is not larger than unity. Some numerical experiments were conducted to obtain a visual interpretation of the analytical results.

AB - Malaria is one of the many kinds of vector-borne diseases which threaten many developing countries around the world every year. Malaria is caused by more than one type of Plasmodium, which allows a superin-fection between two kinds of Plasmodium in the human body. This article presents a mathematical model that describes the superinfection between Plasmodium Falciparum and Plasmodium Vivax. The model is developed as a system of a nonlinear ordinary differential equation which accommodates several essential factors, such as birth and death rate, infection process, superinfection phenomenon, recovery rate, etc. Mathematical analysis regarding the existence and stability of fixed points is discussed followed by the construction of the respective ”local” basic reproduction numbers and the ”invasion” basic reproduction numbers between Plasmodium. We found that the malaria-free equilibrium point will be locally stable if both local basic reproduction numbers are less than unity. Our results also indicate that although the ”local” basic reproduction number exhibits the existence of a single Plasmodium equilibrium, it is still possible that this equilibrium is not stable if the invasion basic reproduction number is not larger than unity. Some numerical experiments were conducted to obtain a visual interpretation of the analytical results.

KW - Equilibrium point

KW - Invasion reproduction number

KW - Malaria

KW - Plasmodium falciparum

KW - Plasmodium vivax

KW - Superinfection

UR - http://www.scopus.com/inward/record.url?scp=85108356160&partnerID=8YFLogxK

U2 - 10.28919/cmbn/5612

DO - 10.28919/cmbn/5612

M3 - Article

AN - SCOPUS:85108356160

VL - 2021

JO - Communications in Mathematical Biology and Neuroscience

JF - Communications in Mathematical Biology and Neuroscience

SN - 2052-2541

M1 - 30

ER -