Abstract
This paper presents the dynamics of mosquitoes and humans with general nonlinear incidence rate and multiple distributed delays for the disease. The model is a SEIRS system of delay differential equations. The normalized dimensionless version is derived; analytical techniques are applied to find conditions for deterministic extinction and permanence of disease. The BRN R0* and ESPR E(e–(μvT1+μT2)) are computed. Conditions for deterministic extinction and permanence are expressed in terms of R0* and E(e–(μvT1+μT2)) and applied to a P. vivax malaria scenario. Numerical results are given.
Highlights
Malaria has exhibited an increasing alarming high mortality rate between 2015 and 2016
The latest WHO World Malaria Report 2017 [14] estimates a total of 216 million cases of malaria from 91 countries in 2016, which constitutes a 5 million increase in the total malaria cases from the malaria statistics obtained previously in 2015
The total death count was 445000, and sub-Saharan Africa accounts for 90% of the total estimated malaria cases
Summary
Malaria has exhibited an increasing alarming high mortality rate between 2015 and 2016. The incubation of the disease requires two hosts – the mosquito vector and human hosts, which may be either directly involved in a full life cycle of the infectious agent consisting of two separate and independent segments of sub-life cycles, which are completed c 2020 Authors. Compartmental mathematical epidemic dynamic models have been used to investigate the dynamics of several different types of vector-borne diseases (cf [1]). Some important investigations in the study of population dynamic models expressed as systems of differential equations are the permanence, extinction of disease in the population, and stability of the equilibria over sufficiently long time.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
