Mathematical Study on Impact of Temperature in Malaria Disease Transmission Dynamics

Abstract

Malaria is one of the most common mosquito borne diseases. Temperature is an important factor which affects the life cycle of the mosquitoes and transmission dynamics of the malaria disease. In the present work, we use SEIR compartmental model for the human population and LSEI compartmental model for mosquito population taking temperature dependent parameters. Basic reproduction number, R 0 of the model is computed using Next Generation Matrix Method. Stability of the disease free equilibrium and the existence of the endemic equilibrium point are discussed by basic reproduction number, R 0. Numerical results are carried out with different temperature levels. It is observed that temperature affects the transmission dynamics of malaria disease significantly.

A Systematic Review of the Effects of Temperature on<em> Anopheles</em> Mosquito Development and Survival: Implications for Malaria Control in a Future Warmer Climate

“…Likewise, as temperatures increased from 15 to 35 °C, the longevity of Anopheles mosquitoes decreased. This is similar to other studies [54][55][56] that reported that mosquito longevity and mortality are negatively affected at higher temperatures.…”

Analysis of the Model on the Effect of Seasonal Factors on Malaria Transmission Dynamics

“…In this paper, a malaria transmission model with temperature-and rainfall-dependent parameters is studied. The present model differs from the models proposed by Mukhtar et al [30] and Bhuju et al [33] in that it assumes that interaction coefficients between humans and mosquitoes are constants and also ignores the exposed class in the mosquito population. In addition, the stability analysis of the steady states is also carried out.…”

“…It is assumed that mosquitoes do not die from malaria due to their short lifespan. Adult female Anopheles mosquitoes lay eggs at a temperature-dependent rate LðTÞ, and the aquatic mosquito population increase is constrained by the carrying capacity of the environment K [33]. Aquatic mosquitoes mature and develop into adult mosquitoes at a temperature-and rainfall-dependent rate λ ðT, RÞ.…”

“…and [30], the maturation rate of mosquitoes to adulthood is temperaturerainfall dependent governed by the total number of eggs laid per adult mosquito per oviposition ωðTÞ, daily survival probability of rainfall-dependent eggs P 1 ðRÞ, daily survival probability of rainfall-dependent larvae P 2 ðRÞ, daily survival [33] Egg deposition rate L T ð Þ −0:153T 2 + 8:61T − 97:7 day -1 [30] Aquatic mosquito death rate μ A T ð Þ 1:0257 − 0:094T + 0:0025T 2 day -1 [30] Interaction coefficient between susceptible mosquitoes and infected humans β V 0.00021 - [42] Adult mosquito death rate μ V T ð Þ −ln 0:522 − 0:000828T 2 + 0:0367T À Á day -1 [30] Carrying capacity of the environment K 1000000 Dimensionless [30] 13 Journal of Applied Mathematics probability of the rainfall-dependent pupae P 3 ðRÞ, daily survival probability of the temperature-dependent larvae P 2 ðTÞ, and the temperature-dependent duration of the immature mosquito development T EA ðTÞ given by ω T ð Þ = −0:153T 2 + 8:61T − 97:7…”

Global Stability of COVID-19 Model: A Case Study of Nepal

“…Mathematical models are useful to study the transmission dynamics of infectious disease and to conduct control strategies against the disease [3,4,8,9,12,13,14]. J. Singh et al used the successive approximation method for short term forecast of infected population in India [18].…”