A Mathematical Model of Malaria Transmission with Structured Vector Population and Seasonality

Abstract

In this paper, we formulate a mathematical model of nonautonomous ordinary differential equations describing the dynamics of malaria transmission with age structure for the vector population. The biting rate of mosquitoes is considered as a positive periodic function which depends on climatic factors. The basic reproduction ratio of the model is obtained and we show that it is the threshold parameter between the extinction and the persistence of the disease. Thus, by applying the theorem of comparison and the theory of uniform persistence, we prove that if the basic reproduction ratio is less than 1, then the disease-free equilibrium is globally asymptotically stable and if it is greater than 1, then there exists at least one positive periodic solution. Finally, numerical simulations are carried out to illustrate our analytical results.

Travelling and COVID-19: A Mathematical Model

“…In second case, when γ becomes maximum, equilibrium level of infected individuals becomes lower but the disease doesn't die out completely. In third cases, when the values of key parameters are taken minimum, then fig (8) shows that the disease may die out completely but the disease free equilibrium point gets stable approximately after 12 -15 weeks. But, when γ is taken maximum, disease free equilibrium point gets stability within 5 weeks and the disease dies out completely.…”

A discrete-time mathematical model of stage-structured mosquito populations

“…Our goal is, after having a fundamental understanding of the dynamics for the mosquitoes, to have the mosquito models incorporated into disease transmission models for the mosquito-borne diseases [7]. There have been many elaborate works for the dynamical behavior of the transmission of mosquito-borne diseases [8][9][10], but many of these models do not take into account the metamorphic structure differences of mosquito populations. As we know, individuals differ in size or developmental stage, they also differ in their vital rates.…”

“…As we know, individuals differ in size or developmental stage, they also differ in their vital rates. Recently, continuous-time dynamical systems of stage-structured mosquito populations have been studied [9,11]. However, since the experimental data of the detection of mosquito population in the field are discrete, we ought to establish a discrete model no matter considering the research background or the rationality of the model establishment.…”

A mathematical model of malaria transmission in a periodic environment

“…Those who have acquired immunity can host and tolerate malaria parasites without developing any clinical symptoms. They may become asymptomatic carriers of parasites and may transmit slightly the parasites to mosquitoes [15,19,34].…”

“…This article is an extension of the model studied in [10] in the sense that we consider the life cycle of vector population and the climatic factors on the biting rate of female anopheles mosquitoes [34]. Thus the model is formulated as a non-autonomous system of differential equations.…”